I think he is giving you mixed messages. He is trying to play it 'cool' and is probably as keen as you but just wants to have the upper hand. It's all very well pretending that FWB is just a bit of fun that doesn't really matter - fine, then pull the rug from under him and remove the 'benefits'. If he's not going to stick with the 'friends' bit, why on earth should you provide the 'benefits' bit? There are umpteen men who would be more than happy with commitment-free sex and I am sure he does NOT have potential FWB queuing up at his front door. I guarantee you he does not in fact. He's just milking the fact that hes having his cake and eating it and you haven't cottoned on to the fact.
You, on the other hand, could indeed have a long line of FWB lining up IF YOU SO CHOOSE THAT.
Honestly, take some of the power away from him and consider replacing him with a few of your own, carefully chosen, FWB. Some of them might be more than happy to be much more if YOU so wish.
Also, why WOULDN'T he want to meet members of your family? Unless they are related to the Kray Brothers perhaps? How RUDE.
PLEASE take some of the smug grin off his face and stand up for yourself - YOU decide the terms. Women have a different relationship towards sex than men and I guarantee you in this particular situation you hold all the cards. Don't let him walk all over you. If he's going to remove the 'friends' bit then you remove the 'benefits' bit.
Think more about you and less about him. I can assure you that if he sees you walking away it will be him that is worrying about losing you.