Why did He Who Remains choose Loki as a possible successor?

Sylvie (and Loki) aren't necessarily the best possible choices for the job - He Who Remains may just be desperate, or too tired to care, or just making a bad gamble.

As this MSN article points out:

he is tired, and wants Loki and Sylvie to take his place as rulers of the TVA.

According to Film School Rejects:

The ancient figure before them has gone a little kooky over the centuries, and he’s looking for retirement.

This article on Marvel.com refers to HWR as a "mad scientist recluse".

Remember that he's lived "a million lifetimes" knowing exactly what will happen, and has suddenly reached a juncture where that's no longer true. He himself says:

What’s the worst that can happen? You either take over and my life’s work continues, or you plunge a blade in my chest and an infinite amount of me start another Multiversal War. And I just end up right back here anyways. Reincarnation, baby.

When Sylvie "declines" his offer, he ominously follows with "See you soon". According to The Wrap:

More or less, what he’s saying here is that the creation of the new multiverse will simply lead to the same outcome where he uses Alioth to end the Multiversal War and then create the TVA like before, like a time loop on an epic scale. But he might be very wrong.

According to IGN, they are reaching the point in time

[...] that will finally free him of the self-imposed prison he has been living in as master of the timeline.

Note: the character in question is not necessarily Kang, but possibly a less evil variant of Kang (or Immortus).

He Who Remains doesn't give much information as to why he has offered this role to Loki and Sylvie.

HE WHO REMAINS: (SIGHS) Buddy… I’m tired. And I’m older. I’m older than I look. This game is for the young, the hungry. I’ve gone through a lot of scenarios… trying to find the right person to take this spot. It turns out that person came in two. (EXHALES) But it’s definitely you two. So, no more lies. You kill me and the Sacred Timeline is completely exposed. Multiversal War. Or you take over and return to the TVA as its benevolent rulers. Tell the workforce who they are and why they do what they do.

One thing we do know is that Loki's hunger is at the right level. He has repeatedly stressed his 'glorious purpose' and his desire to ascend to be God-King. Paired with Sylvie, you have twice the ambition and a creative tension that enabled them to succeed in their mission to unmask He Who Remains. This was part of his 'training' for them.

HE WHO REMAINS: Oh, come on. You know you can’t get to the end until you’ve been changed by the journey. This stuff, it needs to happen. To get us all in the right mindset to finish the quest.

So He Who Remains is looking for an unbridled ambition to be God King, tempered by the wisdom gained by suffering.

Although, this question has been answered, I felt like adding few points for a better understanding. Though, it is bit long, if you're a true fan read it or feel free to skip. I've taken a psychological way to explain this.

• First of all, I want to talk about 'He Who Remains'. I believe we need to understand him to properly answer this question. As per his story, he lived on Earth in 31st century and he discovers the fact about the parallel universes. With all the ambition and the curiosity, he finally meets his variants.

• Naturally they made contact and for a while there was peace. Narcissistic self-congratulatory peace. They shared technology, knowledge, using the best of their universes to improve the others. However, not every version of me was so pure of heart . Now here imagine being in room with versions of yourself and then realizing one of you is a murderer and you don't know who. Imagine the chaos!!

• He dealt this shit for eons which he called 'The Multiversal War' fighting his own versions (who probably knew all the hidden secrets, weak points and knew exactly where to hurt) until he found Alioth.

• But, after ending the war he might have not lost his sanity but he surely did loose his humanity the proof of which is TVA which he created to address the problem of reality branching and had to be dealt with to keep the timeline safe.

• Now, think since he was a human and dealt with these all things by himself which serves as proof as him being alone in the castle in the Void and no-one to appreciate him or commend him, he still grew as a quite a character.

• Therefore, I believe tired is an understatement here.I believe, he isn't just tired but bored as well.

I recited this story to help me support the upcoming points.

• Secondly , Think about his personality, I mean he's like god of tony starks(or more like Rick Sanchez). He mastered not only inter-dimensional travel but time-travel as well. He practically messed (well maybe,corrected) with time as he wished without any repercussions. Do you actually think he didn't see this coming?
• Every genius in marvel universe has their own agenda or morals but in the end all of them (comic reference) loves to prepare for the future. Be it Reed Richards or Dr. Doom.
• He must saw this outcome coming and weighted it very carefully with others to make it more favorable for him.He actually wished this to happen so it did. Maybe to release him or maybe to start another war.
• He rather let the Lokis to choose a path for him than create an anomaly himself (Power Vacuum), so either he has to clear idea where he'll end or he is simply letting go of it this time. But I believe he'll be proven very wrong this time.
• But if Sylvie killing him is what he really wants then perhaps if they would chosen to take his position could have triggered him to show his true face.
• So he's either the greatest schemer ever or just a fatalistic person to choose them.Simple AF!!

• Thirdly, I think Loki was worthy of being his successor.
• As mentioned Alioth, the trans-temporal entity that serves as the guardian of the Void was kept there for a reason.
• Think about it, He's sitting at the Citadel at the End of Time, where no one ever thought was possible and nobody knew about the place not even the TVAs. Why would he be needing protection and from whom?
• Now, I know what you guys might be thinking. He's there to engulf the pruned ones. But what if it was the other way around, to keep him there the pruned ones were send there. He Who Remains is genius, he could always would have taken care of pruned ones one way or the other. But this situation was a win-win for him.
• Now coming back to point, After watching the battle with Alioth it's very obvious that physical attacks don't work on him. So I can fairly say that even the Avengers (Big 6) wouldn't be able to defeat him cause you know, they can't mind control him.
• With the current characters in the Marvel Universe, I think only three people could take him one-on-one : Loki , Scarlet Witch or Dr. Strange. The Loki's battle is sufficient to say they were quite capable of defeating Alioth.

I know this is quite an explanation, but just because it's long don't use it as an excuse to not read it properly.
Adios :))