Well I think the answer to that differs from person to person but I believe the fundamental reason is the difference in societal experiences between the generations of the parents and that of the children.
Parents are often brought up in different times from their children and the core beliefs of each generation differs greatly. I mean a kid could be told by his parents that if he goes to school and gets a good degree he'll be able to get a great job and live the American dream, but on his/her own he might find out that in this time and age, it's not that easy.
Now this may have been true in our parents time and age but it's not so true anymore these days and that's because times have changed. The difference in experiences between that of the parents and that of the children is what to me is the major reason why they have different opinions.
Parents have opinions that are based on what they've experienced and children will have opinions based on what they've experienced as well. Because of the difference in the two generations, there's bound to be a clash of opinions.
I hope this helps.
I think it all boils down to past experiences on the part of the parents and the new excited non-experienced youthful children. Parents through their many experiences in life, have made some mistakes, identified some bad habits, had some regrets, made wrong choices etc. So it is very normal to see them do everything they can to make sure their children do not repeat thesame mistakes while on the other hand, we have youthful children who just want to enjoy their lives to the fullest and are ignorant of the dangers of their actions.
In their ignorance and quest to live their lives the way they want, their parents who are also bent to guide them will always clash with them in their opinions and beliefs about life. In most cases, these opinions and beliefs are opposite among the two groups. For example, parents will not want their child keeping late nights believing its not safe but on the other hand, we will have a youthful child craving to attend a late party and seeing nothing wrong with that.