I thought it was pretty obvious why Jon 'has to know'. It's clear at this point that Bran's purpose is to help defeat the Night King. He knows he's the chess player, and he knows he needs to make the right moves. He isn't thinking about Jon's feelings, or how many times him and Dany are going to do the naked dance of dragons. We know Jon also has a massive role to play in defeating NK, and Bran realises Jon needs to be Aegon Targaryen to fulfill that role. Can't see there being any more or less to it than that. I imagine pretty much everything Bran does or says from now on will be him moving another chess piece to where it needs to be for the checkmate on his opponent.