Why did Harry choose to save Draco Malfoy during the battle of Hogwarts?

Because he has a "saving people thing". He wouldn't have been able to let anyone die, even a person he doesn't particularly like, like Draco.

Even though they weren't friends, they grew up together in the same school. Maybe Harry just disliked Draco, not hated him. So, it might be that he didn't enjoy seeing Draco get hurt. well, I wouldn't enjoy seeing a classmate die au get hurt, no matter how much i don't get along with him/her, especially when there's a chance that i may be able to save him/her.

Because it's Harry. He saves even people he nearly hates. He's the definition of a virtuous person.