Pulls existence from the void
This point is highly dependent on whether or not you believe there is some sort of soul or existence before birth. I cannot argue on this point since this is pure belief, so I will accept your view for the sake of the discussion
Questions how not doing so could have prevented suffering
You could say it prevents suffering, but it also prevents Joy, Love, Friendship. Sure it also prevents Sadness and Grief and so on. It prevents everything by way of not giving life a chance.
If you think you cannot provide a happy life to your children then it's perfectly valid to not want children. But it's egoistic to think that other people should not have kids because of your own world view.
Many Antinatalists believe that life in the current world is filled with so much suffering that it's not worth being born.
But that's like... Your opinion man! Let people make their own choices
There are not many occasions where someone would accept a fish as a gift. But having a mechanic say "Gift a fish" is pretty funny