My boyfriend is too private

I’ve been with my boyfriend for 2 years and for the most part we talk about personal things but I still feel like he’s holding back. I know he didn’t have a perfect upbringing but when I ask about things like his family or his past he gets touchy or he says oh I dont remember, and it makes me feel a way that he doesn’t think he can trust me. He’s had another long term relationship maybe he just closed off after the first one ?? Maybe this is just him ?? I’m big on opening up and I need us to be closer. I don’t know what to do