Yes, you are rushing.
I’m pretty sure that’s not what you want to hear, but that’s what’s going on. For some reason you’re very anxious about controlling the relationship rather than letting it take it’s own course in it’s own time. While it’s clear you want more, it’s also clear your boyfriend thinks things are going too quickly. The relationship is the sum total of [i]both[/i] of your feelings and actions. If you try to commandeer the relationship and force your boyfriend into living together before he’s ready, he’s going to react negatively or act out at you creating drama and fighting.
So take a step back, even though it’s scary to you to go from “faux” living together to “just dating”, and see how things progress on a more natural time frame, namely one where both partners’ feelings are taken into account. I think that the age difference between the two of you doesn’t have to be an issue at all, but I think at 29, your boyfriend is taking this relationship more seriously, ironically. He doesn’t want to rush into something he’s not sure about. And I’m sure you don’t want to rush him if it means the relationship backfiring on you. If he’s not introducing you to his friends or family, he’s not taking the relationship that seriously, and moving in together under those circumstances would be a mistake.