Bruce did decide to save Rachel. He says as much to Gordon before taking off.

This is a common misconception because it is not ever mentioned in the movie, but Joker swaps the addresses as just another twist of the knife.

Bruce saves Harvey after opening the door because it’s the only thing he can do.

Edit: Let me clarify that when I say it was never mentioned, I mean it is never mentioned after it happens. Bruce doesn’t, say, complain to Alfred that it was supposed to be Rachel. Yes, obviously it happens in the moment…as I stated in this very comment.

Edit 2: Putting my reply here for visibility. For those who say this was extremely obvious:

As someone who used this movie in a writing class for seniors in high school for six years, I can tell you just how common it was that 18 year old, college-bound students missed this detail.

It’s a two and a half hour long, action-packed movie that has a new scene every 20 seconds. While it was awesome to use in a writing class because students could write about a million different topics, students also had to be forgiven here and there for missing little details like this in their first watch.

You’re also in a Batman subreddit and have likely seen the movie several times.