I can't convince myself of my depression

I keep telling myself that I'm depressed, and that it's a disease, but I have so much trouble actually convincing myself of that. I think that I've struggled so long with these feelings of worthlessness and of not being able to make strong interpersonal connections that I've internalized a lot of it to the point that I feel like the depression is intrinsic in who I am, and that I'm the one to blame.

It's so easy for me to look at other people, and believe that depression is an actual disease; but, when I look at myself, I just can't see it. To me, the constant thoughts of killing myself seem totally rational. We all live and we all die, so what if I want to skip most of the living part because I'm lazy and tired and don't want to keep trying?

I just have these competing sides within my mind. One is saying that you're fine, you're just weak and searching for excuses for the shitty person you are; the other side is whispering you're sick, but maybe you'll get better. I just can't reconcile them. And in a weird way, I know that I'm depressed because I'm convinced that I'm not and my mind just keeps going with this eternal battle, each side undermining the other. It's confusing, and frustrating, and difficult because I don't know where my mind and my thoughts end and where the depression begins, or if they're just one and the same.