Why does it hurt...

Probably because his admitting to it leaves no more chance of it not being true. Even though you suspected and then found facts confirming your suspicion, in your mind, there's still that tiny shred of hope that he would say it wasn't true and somehow prove it. You never want to believe something painful is true. So, you may (even subconsciously) hang on to any chance it isn't regardless of how unlikely or ridiculous it is.