My boyfriend wants me to see a psychiatrist, but I don't think I need one?

He thinks it would be good for me. We're 20 and 21 and have been in a relationship over a year. He was clinically depressed before, although while we've been together he's been happy and alright. He's had a few breakdown episodes during stressful exam periods, though. I was there with him and tried my best to comfort him.

However, it's me he's worried about. I've always had self-esteem issues and over our time together I've often felt sad or guilty about things I can't change or just felt really bad about myself for no reason. I would cry when he was elsewhere and I've also been very emotional with him as well a few times, to the point of tears. Thing is, even though I feel unsure or sad, I've never really been depressed. I see all these people with problems so much worse than mine and everything I feel sad about feels like nonsense then. My boyfriend doesn't get it that with his talk of how I need a psychiatrist, he's just driving me further away. I do not wish to see a psychiatrist, neither do I need one. Am I being unreasonable or is he right?