I just wanted to put the otherside to this problem, I have experienced this from both sides.
I believe it is all about unconditional love.
As a young person living with one parent and visiting the other I used to hero worship my Dad who is actually a crap parent. He never said no to me, bought me treats and seemed pretty much perfect.
Mum on the other hand was always there, she was the solid person in our lives but obviously she made us do chores and told us off from time to time oh and of course she regularly said no.
However she was reliable and didnt mess us about and guess what, no matter what we said or did she still loved us and continued to be the same parent she had always been.
I am not saying my relationship is perfect with her but guess which parent I am still in contact with.
Please try not to take it to heart, they are in a difficult situation too, always trying to balance 2 lives is tough.