Why did the rebellion allow Katniss to enter the Hunger Games a second time?

I think there are a few reasons behind this.

Firstly, it allowed Katniss Everdeen, the symbol of the revolution, to be seen and admired by all the Districts. Her appearance as a Mockingjay before the 75th Games began would have been inspirational to all the fighters in the Districts. It sent the message even though she couldn't avoid the Games and couldn't avoid another fight, she was taking it head on and being herself - not the girl-to-be-married Snow wanted her to be.

Secondly, it allowed all the undercover games entrants to be collected from the same location. Although they knew each other before the Games began, this game the Rebellion the opportunity to get all of its former victors in one place at one time and evacuate them all.

Thirdly, and perhaps most importantly, this all happened on live television. If Katniss had joined the rebellion, or rather been rescued by them, in the Capitol, before the Games began, the Capitol would have suppressed the information and released a cover story. With Katniss disappearing in front of the world and the Games - which are used by the Capitol to display their superiority over the Districts - being blown apart (literally), the world knew how serious the Rebellion was and how strong it was. The message this act sent was powerful enough to risk Katniss.

This is a theme that gets explored further in the third book, when they bring Katniss out into the warzone on different occassions. Although they don't really want to risk her life, they want her close enough to the action for her to be inspirational and symbolic as the tough freedom fighter the rebellion's members think she is.

To conclude, imagine famous scenes from real-world history, such as the Tiananmen Square image - and now imagine the powerful effect they've had. I believe Katniss' appearance in the Games was intended to have the same effect. Whilst the first two reasons above are important, the third reason was the crucial one - her escape from the Games well and truly demonstrated the strength of the Rebellion for the first time to both the Rebellion's members and the citizens of the Capitol.

After the victory tour, President Snow sees the effects of Katniss on the Districts and the riots. He was planning to eliminate her, but Plutarch Heavensbee offers to take her into the games to give the districts a message: Even the strongest among all are weak against the Capitol and even they can be killed easily by the Capitol

So the Quarter Quell game had changed, and all previous winners are invited.

A speech between Katniss and Plutarch in the 74.th Hunger Games Victory Ball:

Katniss Everdeen: "Then why are you here?"

Plutarch Heavensbee: "Same reason as you: I volunteered."

Katniss Everdeen: "Why?"

Plutarch Heavensbee: (shrugs) "Ambition...the chance to make the Games mean something."

Katniss Everdeen: (contemptuously) "The Games don't mean anything. They only mean to scare us."

Plutarch Heavensbee: "Well, maybe it was you who inspired me to come back. (a fanfare sounds) Ah, the Presidential welcome. I'm sure we'll meet again."

So, the only chance Plutarch had was to help Katniss and to support the riots to put her into the games. Otherwise, Snow will get rid of her in some other way.

But in the books, the situation is quite different. At the Victory Ball, after dancing with Katniss, Plutarch Heavensbee shows her his watch. For a second, Katniss saw a mockingjay on the watch, which disappears afterwards. Plutarch tells Katniss that the watch is important and valuable.

After her rescue from the Arena, Plutarch tells her the reason he showed her his watch was he was expecting to see Katniss as a Mentor of new tributes, not in the arena as a tribute.

So, Quarter Quell tribute plan all belongs to President Snow, and the rebellion has nothing to stop Snow. Only thing they can do is arrange other competitors so they can help Katniss stay alive in the arena. Johanna concusses Katniss to remove the tracker chip so she can be rescued by the rebellion and not captured by the Capitol etc.

As per my speculation, the rebels allowed Katniss to enter Second time to send message to all 12 district about rebellion. Do you remember her dress conversion into Mockingjay, that must be a message to all about the coming rebellion. In the Hunger Game world, districts can't contact each other but the games are a good way to send messages to all districts.

My second thought is that they didn't get the right opportunity before. Katniss is now a star and people see her, follow her and a TV channel also covers her. Her disappearance need to be pre-planned. The 75th game was surprise for all, so they didn't have time for her escape plan.

But I more strongly believe the first one where the rebellion wants her to be a Mockingjay symbol for all by participating.

It wasn't a miraculous breach in the dome either! The plan was always for that genius man to sacrifice his life and shoot an arrow at the dome when lightning struck. It was only once that guy was killed that Katniss realised what he was trying to do and done it for herself, also if Katniss wasn't put back into the hunger games then they would have just gone on as normal- therefore completely ignoring this "uprising"- Plutarch Heavensbee had been planning this revelution for years and was waiting for the right time- after the riots in the districts etc after katniss defied the capitol he knew it was time. Putting victors back into the games made the districts even more angry, and having all the extra added on violence from the capital and "peacekeepers" made people in the districts even more scared and angry. Whether Katniss lived or died she was put back in as a symbol. - the uprising was already happening before, this was just the spark to set it off.

There is a simple reason for this and one of the reasons they don't let Katniss know about the plan. It's that if she lives, she can be a symbol to hold up to all in the Districts. If she dies, she becomes a martyr, which is an even larger symbol they can rally the Districts behind. Either way, they have what they need. Katniss is just a pawn in the whole ordeal. Albeit a willing pawn, but a pawn nonetheless.

I found some explanations in the books that reasonably apply to the movies too.

The rebellion wasn't full-fledged when they had the announcement of the Quell --

"It means we're on your side." That's what Bonnie said. I have people on my side? What side? Am I unwittingly the face of the hoped-for rebellion?

District 13 wasn't willing to risk another war prematurely. They needed other districts' cooperation to have a chance against the Capitol, and the other districts were not yet in total rebellion at the time of the announcement. Furthermore, they may not have been strong enough yet to operate out in the open against the Capitol:

I feel that twinge of hatred against 13 again. "So, you had all this, and you left the rest of the districts defenseless against the Capitol." "It's not that simple," he shoots back. "We were in no position to launch a counterattack until recently. We could barely stay alive. After we'd overthrown and executed the Capitol's people, only a handful of us even knew how to pilot."

It seems they got their plans in order quickly, though, based on Haymitch's explanation at the end of Catching Fire.

There was a plan to break us out of the arena from the moment the Quell was announced. ... We are currently on a roundabout journey to District 13. Meanwhile, most of the districts in Panem are in full-scale rebellion.

And everything fell together at that point. Many districts were in full rebellion by then, certainly fueled by the emotion of the 75th Hunger Games (the interviews, the Victors' hand-holding, etc), and 13 was clearly strong enough to come out into the open and wage war.

It would seem like a much safer approach to have just taken Katniss to a secret location as soon as anyone knew they were planning to have the Victors re-enter the games.

Logically this is what they would have wanted, but it was impossible. Katniss, like all the other Tributes who survived, was heavily tracked and guarded. For the first year after winning, the Victor is paraded around from district to district. We see this at the end of the first movie, and the beginning of the second, as Katniss and Peeta travel by train. Then they normally become possible Mentors for others from their District, as well as fodder for public entertainment. Worse, the Victors become tools for Snow and the Capitol, which we learn in Mockingjay that he sells them for political favors. There is no free or alone time.

But worse, Snow is concerned about rebellion, especially from Katniss. She's doubly guarded and her family & Peeta threatened, personally, by Snow. And as she is still in the Victor stage, she is not in a position to be easily taken away.

The only way to get to her is in the relatively secluded situation that is the game arena. No guards nearby, insider sabotaging the games and security, secret agents that help remove Katniss.

Plutarch: Stop. Just listen. We couldn't tell you with Snow watching. It was too risky. Better for you to know nothing.

Katniss: Where's Peeta?

Plutarch: Now, Katniss... You have been our mission from the beginning. The plan was always to get you out. Half the Tributes were in on it. This is the revolution. And you are the Mockingjay. And we're on our way to District 13 right now.

Katniss: 13?

Plutarch: 13. Yes.

Katniss: Where's Peeta?

Plutarch: He still has his tracker in his arm. Johanna cut yours out.

Without all the distractions of the explosion, of the violence, of the lack of guards, they could never get Katniss' tracker out, and bringing a tracker to District 13 or on the hover jet would be fatal to the Rebellion.

In short, the Rebellion had no way to extract Katniss without letting her compete. In fact, without the 75th game, they would likely never have gotten her at all. Remember, they could only get into the Capitol in Mockingjay after all power was dropped, including the border defense systems, and even then only when Snow let them. They wouldn't have been able to extract Katniss from the Capitol by force or by covert means.

Not to mention we would have missed a couple hundred pages and a couple of hours of awesome if that were the case. The third book would essentially just merge in to the second...

But, in all seriousness, I like Andrew's answer. I also don't think Katniss would have let that happen. She's the kind of character that tackles things head-on, and will do whatever it might take to avenge the past and make way for the future. Whether she is to be a martyr or a hero, she is the character who will be either, but she would not be okay with being stolen away before she could get her message out to the world.

It's not just a matter of the rebellion "taking her". It's also herself as a character.