He lost his parents and he was inspired to make sure that never happens to anyone else so he dedicates his life and fortune to that cause. He knew that Gotham was corrupt so he wanted to get the people who can break the law with no consequences but he can only do that if he was trained so he did.
That doesn’t sound insane that makes him sound very dedicated.
“Oh but he wears a giant bat costume!!!” Yeah a giant bat costume that’s bullet proof and is more expensive then majority of vehicles. Why is it weird that he wears a bat costume you don’t see anyone call green arrow crazy for what he wears or black canary or nightwing. Why is Batman the one labeled as crazy for that reason.
“Oh but Bruce Wayne is the mask and Batman is the real person, he must be crazy” So he’s crazy because his real personality is of a caring, cold, and dedicated man that’s putting on a mask for the public to hide his life of crime fighting. Im sorry but that just means Bruce isn’t someone who likes to sleep with every pretty lady or likes to have extravagant parties.
I don’t see how he’s crazy.