I have heard many people of Indian descent lament the fact that their children do not speak their 'native languages' as well as they should, or appreciate the food that they themselves grew up with. However, I think we are making a mistake in confusing children who are rejecting culture with children who are at an age where most need to rebel in order to learn.
We will always pick and choose which aspects of culture are maintained from generation to generation, just as people pick and choose which aspects of their religion they are comfortable with. For example, for some, cutting the hair on their heads is a grave mistake; but their beards and mustaches will be impeccably kept. Others think that loving certain kinds of people is wrong, but they'll eat things that their religion supposedly forbids. Similarly, there will be certain parts of culture that will always appeal to us more than others.
For those who are worried that appreciation for culture is dying out, think again. As long as humans appreciate the importance of place, love, emotions and the things that make us feel and tie us together, culture will still be highly relevant in society.
I speak from experience of course. As an Indian Kenyan, I've come to realise we have a culture of our own. We're multilingual. We appreciate (and claim) many different kinds of food. Art is important and revered. We dress up in certain ways for important occasions. Indian Kenyan-ness has such a richness to it that's hard to describe in words. And at the end of the day, we know that we have an identity that we can uniquely claim as our own.