I try to find out why. Is it based on my fault in some way then I exain I want to learn from it, so I ask what I could have done better, plan to do just that and say sorry.
So... Do they feel let down? were you not there for them in an hour of need? Did you show disrespect for their values, what they stand for, or who they are? Did you talk about them to other people? Break a confidence? Did you treat them unfairly? Punish them or someone else for something which was not their fault, or just a mistake? These are all yhings which I think a child of mine might ferl justified to feel hate for me, and I should apologise for if I did them, even unintentionally or thoughtlessly.
Or... Is it more that they hate tgemselves, and are projecting it onto you? Hate their lives, hate their lack of choices, lack of control over yheir lives?
That is understandable. That needs a rienforcement of their self esteem, encouraging them to develop and maintain good self care habits, respect and enabling them to live out their valurs wtc.
Or.. Do they have values so different to your own that they hate your choices, your appearance or behaviours, what your values are, how you live your life? Then they need help expressing themsrlves and understanding the boundaries of ones own choices and responsibilities. Taking credit only for ones own achievements, giving them complete credit for theirs, and the same with mistakes, self harming and destructive habits, etc.
There's a lot there, there are probably many more reasons why they say these things, and it might be different each time they say it. It is sometimes a sign to get to know them and give them chances to learn things like driving, cooking, leadership, caring etc and help them get paid work, if that hasn't already happened. For others, it is a fleeting passing phase which has no deep meaning and which is soon forgotten if not too much is made of it.