Why does Jeanie help Ferris out at the end of Ferris Bueller's Day Off?

I never really considered it to be a territorial issue as much as it was for her to seize the only win-win outcome for herself:

Jeanie already faced-off (or rather, kicked in the face) Mr. Rooney, mistaking him for a normal burglar. Seeing that he was correctly pursuing Ferris for truancy (meaning Ferris was truant, not that his methods were justified)--and knowing the futility of law enforcement in the situation--she claimed her win over Mr. Rooney here by excusing Ferris' behavior and absence, which Mr. Rooney could not contest.

With Ferris, it is true she failed to justify hers and Ferris' inequitable treatment, as we remember from her voice-over in the school hallways ('why should Ferris get away with everything? ...after all I got a car, he got a computer...'). But, I speculate that getting home before Ferris would be her way to gain leverage over him.

The opportunity, however, to humiliate/deprive Mr. Rooney and indebt Ferris ultimately was probably more appealing than the inevitable shattered, broken happy home that would occur when their parents' found out he isn't such an angel as they believed.

When you have a little/big brother or sister, you hate them...you would do anything to get over on them or even hurt them sometimes...but when someone else tries...they become YOUR territory that is being threatened...you should defend your territory. This was Jeanie's knee-jerk reaction.

I thought the motivation to switch to Ferris' side was pretty clear. Her mind was changed while she was in the police station chatting with the cool and laid back character played by Charlie Sheen (see it here). He professes a philosophy of live and let live and tells her that she is the problem—not Ferris. She rejects the advice several times, but eventually embraces it when she falls for Sheen's character.

Basic psychology - students rebel against authority (even the goody-goodies). Giving Mr. Rooney a win was not in the cards. "The enemy of my enemy is my friend." To paraphrase - Ferris, the enemy of Mr. Rooney, is my friend.

The basis for Jeanie not giving up Ferris is quite simple, if maybe 2-part: You have a person in your group not well liked and it shows. Some outside your group wants to abuse that person. It becomes territorial. "He maybe a jerk, but he's our jerk". Mixed in with that a bit of the enemy of my enemy is my friend. Basic? No doubt. Simple? Yes indeed, as are most truths in life.

She found Rooney's wallet in the kitchen and realized he was the reason she was so scared and wound up at the police so revenge against Rooney overcame her need to get her brother. After all she could always get Ferris another day. ;)

I would say that her biggest gripe against him was that he never got caught and that life didn't seem fair for her because he always got lucky and she didn't. When she beat him home, she enjoyed the moment, and then realized she had won, and that she COULD get him in trouble if she wanted to. That was enough for her. She didn't actually want to destroy her brother - she just wanted to know that she could win against him, and that his luck wasn't always perfect. Being the one to save him was part of it too because she felt even more powerful in that moment. She didn't want to actually hurt her brother, she just needed a win.

Y'all are missing it. The enemy of my enemy is my friend.

She got arrested over Rooney being in the house. She was in the right, yet was busted and not believed. It combined her and Charlie's meeting in the police station with her pursuit of her brother. She saw in herself Mr. Rooney and wanted to be more the girl that made out with the thug. She also finally saw what people see in him. He was a fun, popular guy. Their common enemy finally awoke her inner Ferris.

Ferris has finally been caught. Remember Jeanie is mad that Ferris gets away with ditching. So now that Ferris is caught, she is satisfied, and at the end if the day they are still family.

I think the winking eye is way too much in that scene. That does not fit in the brother sister relationship shown in the rest of the movie. On the other hand, Ferris is one lucky guy... even his enemy supports him in the end, which surprises him too, hence the way he looks at the camera.

From Jeanies point of view: Saving Ferris makes him owe something to her.