I've gone through the same series of thoughts about resenting my parents for having birthed me as well. And other things as well, however I'll focus on the birth since that is what is relevant here.
Your feelings are valid. 100%. You would not be depressed if you were born. You never asked to be born. And your parents had you despite being aware of (or negligent of) creating you would result in you having to go through the suffering that is life.
(Skip the next two paragraphs if you want my knowledge on how to stop it.)
Ultimately, conceiving a child is a selfish action. For two parents that want a child, they either subconsciously (or consciously) acknowledge that they are creating another being who will go through the same suffering they go through that is existence. For two parents that have a child by mistake and abandon it, that's even worse. They not only have done what is above, but are letting that child fend from the world, who never had a say whether or not to be there, fend for itself in it's most vulnerable state. Some though are just blissfully unaware and caught up in the moment, which is quite negligent considering you are conceiving a new being that will have to deal with all the stresses of the world. A lot of people think like this however. It's "the next step in life" to start a family, have children... It's deep-rooted into not only our society but our drive biochemically.
For those who say it is for society and therefore makes it less selfish, how about all the way back in history when human sacrifices were a thing? When they would brutally murder one or multiple human beings just for the "greater good"? The gravity of those situations may be different but the concept is the same. Both acknowledge the suffering one will go through for "the greater good" (albeit one is more demented than the other). They thought that whatever Gods they believed in would grant them flourishing crops or good weather to survive the next season or whatever. In this case, two people have a child for the "greater good" of the human species. Even those who want to see just want to see their children happy are still selfish since that child never exactly had the say so in wanting to live their life.
So, being that you are in this world of suffering all the time, how can you stop resenting your parents for giving you this terrible existence?
-Well just like you and I, our parents were subjected to the same scenario of being conceived into a life they didn't ask for either. They perhaps have gone through some extent or a lot of suffering as well. I know my Mom and Dad have, and that's probably why I've been here longer, to help them (even though I will depart from this world soon).
-Maybe taking a look that they were also born unwillingly may help alleviate that feeling. If they have done you more wrong though in your life, this solution may not be the best.
-This may not be possible given your circumstances, but find reasons to enjoy your life. If you can enjoy your life more, you will look at your life less and less as a resentment and more and more as a "blessing". However, I believe that most of us that have reached this forum are far past this point. (Also telling a chronically depressed person to be happy is like telling someone with a knee injury to walk, it's really hard for them).
I can see that you are on a journey to recover. In closure, you are resenting your parents because you are depressed in your life, and they have given you that life. If you are happier or less depressed, you will resent your parents less since happiness is not something you resent (it is what we want). I wish you well on your journey to recovery. I send my best wishes and love to you.