We do have deep conversations but I'm more able to have them, and for longer, than him.
He can have a long detailed conversation about facts, history, and practical possibilities, but if it comes to talking about personal, sad things, or vulnerable love emotions, or worries, fears, etc. He really struggles. He also comes from a horrendously unemotional family where gift giving and guilt tripping are the only forms of affection that are allowed.
When we were first dating and he wasn't in love with me he'd talk about anything and listen to any of my worries, I used to think he was an amazing listener and conversationalist!
Then he started to love me, and almost instantly became totally unable to listen to me talk about anything that he even slightly expected might upset me. Because in his family, love means keeping it light and cordial, including changing the subject to something lighter when someone you love is down. They consider it unkind or self indulgent to "pry" or "upset" a loved one. In practice it means someone can literally die in front of them, and they pretend they are fine with it.
I noticed this, whenever I'd talk about something really hard, he would make an awkward joke, but his whole.demeanour would change to that of a scared little boy. I told him it was horrible and dismissive to do that when someone was sad. He was shocked. We talked about it at length and worked out the family habit that was underlying etc. Took a few hurt feelings and a few returns to the same situation.
That was a good three years ago. He now has worked to the point where he notices he is about to change the subject or make an awkward joke, etc and is able to stop himself. He is working on just being ok with not saying anything, or a stock phrase like, "that sounds hard" or "I'm sorry". Its been a huge slog for him.
I still have to check in and sort of say hey, are you feeling up to a chat about emotions, because if hes tired or feeling down, he won't be able to sustain the conversation. The fact based chats are fine, but feelings, it's just a lot of anxiety and hard work and concentrating for him.
"Deep" conversations are definitely hard work for many folk, and I completely accept that many people just dont want to have them. I need to be with someone who is able to have a significant kind of conversation though, not just about facts or events but also about feelings, so it's about compatibility really.