People here are focusing a lot about how to get stronger legs. Why does not the focus lay around the muscles in the stomach?

I think core and leg strength go hand in hand - there is no use in having super strong legs if your core isn't strong enough to lift them, and having a strong core won't help if your legs aren't strong enough to be independent. But I think it's easier to become focused on your legs because that's generally where you feel the pain!
Core strength is more important than leg strength so yeah I've become confused with this too :/
Having a steady leg with jumping etc
Your legs are your anchor if your horse suddenly bolts or spooks, so it's important to have strong legs. Stronger legs also mean less effort put in to give strong forward cues. Having a strong core I would say is most important though because it helps you balance and be lighter for your horse.
I've noticed this as well! I always thought core strength was more important than legs
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