There is never going to be an answer for your parents' behaviour towards you. By that I mean they will never be able to explain why they rejected you in a way that any reasonable person would accept.
The job of parents is to look after their children, not reject them, no matter what the child does and, frankly what on earth could a young child possibly do that would make a parent reject them? Remember we are talking about you as a child here, not you as an adult.
There could not possibly have been a fault on your side, the problem lay (and almost certainly lies) squarely with them .
You may still decide to track them down, but be sure that whatever fantasies you may nurture in the deepest recesses of your mind, they will not have a reasonable and acceptable answer for their behaviour and will not have deeply regretted giving you up. Sorry to be so plain spoken , but if they had deeply regretted giving you up they would have got you back. These people are part of your past and do not deserve your love/care/concern. If you do track them down, please let it be so that you can confirm that they do not deserve you, not to make any kind of effort to find love from them.
Again, very sorry to be so blunt, but you have been hurt enough and I cannot see that you will get much in the way of answers ...at least not those anyone in your situation would most want.
You sound to have truly risen above the experiences of your youth and I hope you can see yourself for the lovely person that you are....and almost certainly were when you were younger too.