Practical and completely non-philosophical refutation: If one of my children makes this argument to me, I'll slap them around the face and blame it on my parents.
Practical refutation 2: Police officers, bosses, judges etc. don't accept that argument so it won't help you much.
Practical refutation 3: If you make mistakes, you can blame these mistakes on your parents all you like, but that's not going to improve your situation one bit, so you better do something to improve your life instead of trying to shift the blame. (In practice, this argument often needs to be used when the parents actually might be at fault for the way they raised their child, but the child needs to be reminded that finding someone to blame doesn't actually improve their situation).
Philosophical refutation: You may be right, but by claiming that your mistakes were already predetermined at your birth and you had no choice but making them, you give up the right to call yourself a human being. Worse for you, if being born is so awful that you blame your parents for it, that is a fixable problem. (Imagine instead of a child a robot who was created and programmed by a person. That person would have to accept blame for damage caused by the robot, and would probably decide to turn the robot off).
Philosphical refutation two: If you claim that your parents are to blame for all the bad things you do, then surely they are the ones to praise for all the good things you do. So when you you get your next salary, you better send that straight to your parents because they deserve it.
Philosophical refutation three: Being born is a necessary precondition for you to be able to misbehave, but it's not the cause of your bad behaviour. As evidence, there are millions of people who were also born but don't show the same bad behaviour. Even if it was the cause, we pass blame only for foreseeable consequences of actions. Your misbehaviour was not foreseeable when your parents decided to have a child.
So there are two entirely different kinds of refutations: The last one just shows that the argument is wrong. Other refutations say that you may be right, but you haven't quite thought through what the consequences of being right are - and if you are right and think properly about the consequences, you'd be very quiet about this and not draw any attention to it.