How important is it to deal with childhood difficulties in therapy?

I definitely have not experienced “big T” trauma, but I’ve for sure experienced some hard things in life as everyone has. My T has occasionally used the words “relational trauma” and “emotional neglect” and has described me as “sensitive” and I’m just having a hard time with all of these labels because it feels like he’s trying to make things seems worse than they were. When I said I don’t think my life was any worse than anyone else’s, he replied, “I think it was.” But I genuinely disagree. And even if it was, I feel like I’m over it. I know my parents loved me and did they best they could even if they were not completely aware of my every emotional need. But he seems to be encouraging me to keep bringing things up and last week he said something about not being able to move on emotionally until we process certain things from our past. He commented on how I try to protect my memories and always say things like “I’m fine” or “it was normal” or “I’m just an introvert” when he tries to talk about certain situations both from my childhood and adult life. I’m just not sure what I’m supposed to do here. I’m trying to figure out how to do therapy and I like my T, but I don’t understand this part. I don’t feel the need to complain about my mostly average past. It sort of feels like some cliche therapy thing to bash your parents and I’m just not feeling it. Not looking for therapy-maligning comments. Just trying to figure this out.