Luke was a whiney ass farm boy whose guardian was strongly opposed to any training. Leia was already part of the fighting from a young age, Bail Organa would probably have been more open to the idea of training her - plus lets face it she's probably quite a bit tougher. So why train Luke instead of Leia?
This is the problem with filling in every single gap in the story with existing main characters over the course of 40 years. Originally (when even Lucas hadn't decided to make them siblings yet), it was implied that only Yoda knew about Leia. (He contradicts Obi-Wan's "that boy is our last hope," which to me implies Yoda knows about her and Obi-Wan doesn't.) Of course that started to erode pretty quickly, and only accelerated with the addition of TV shows to the canon, so now we have Leia going on an adventure with Obi-Wan when she was 10. MAYBE the explanation could be that a latent Force user is hard to detect, but the Emperor and Vader would notice an active Jedi, especially a trainee (maybe Obi-Wan and Yoda had techniques for disguising their impact on the Force, plus Legends suggests that the Dagobah cave helped Yoda hide). So training either of them before adulthood would have just put a target on a child's back and they would have been killed. It could be that Obi-Wan intended to train both when they became adults, but never had the chance. The reason he looked after Luke instead of Leia would then be that Leia, as the daughter of the viceroy, would have plenty of protection, but Luke's only protection was obscurity.
Duh, the god of the universe was trying to sell his universe to the similar gods to him, and at the time they really only wanted white male heroes. Or in other words hollywood would not have bought a force powerful heroin at the time, and was still addicted to the damsel in distress so lucas gave them a male hero. You are thinking way too deep into a universe that was never established beyond the present money grab moment. Let us remember that a lot of drama on the screen really comes down to because the creator thought it would be cool or sad or whatever feeling they were going for.
Leah is the daughter of a prominent senator and therefore exposed already. Luke is in obscurity and can be trained in secret.
On the other hand, Leia has the advantage that low-level flunkies can't spell her name correctly, so she'll slip past Imperial Intelligence (which is an oxymoron).
Although Obi-Wan really didn't train him. It seems like he was mostly just hanging out in the desert, making sure that Luke didn't die (maybe staying alert to any signs that Palps or Vader had detected him?) ... he didn't teach Luke a damn thing until he got Leia's message and they were in the Falcon on their way to Alderaan.
I am sure there are no decent in universe reasons that are not just proving why you should flesh out your characters when you write. However, Star wars fans are the dumb side of sci-fi and will slurp up whatever shit writing there is as long as there are lightsabers and laser blasters. Oh, and let us not forget the most trash character in the universe Boba Fett. Oh my he is dark and mysterious, and that is because he is a fucking extra that made fanbois squee. Now we have mandalorians and armies of clones all because Vader used bounty hunters at one point.
