Culture is what we do and influence others to do habitually, based on principles that we share. So culture is not something we are born with, but something that we are always (in one current form or another) born into.

But the individual still makes his own culture, hence why we have subcultures.

I think the risk is going to the extreme and promoting "multiculturalism" when one actually just mean that people should have a right to behave as they like and exchange cultural information as long as they don't harm anyone. This makes society better, if we adopt the right principles.

Just mixing a bunch of different cultures because we make a badly thought through decission to value them all "equally" (they could be equally good, bad, extreme, mediocre etc) is a very bad idea however. Then we're just avoiding making a decission as to what is right and wrong. With such thinking there is no longer even any known reason to resist dictatorship or other horrible practices.