I definately agree that culture is entirely taught, though not necessarily indoctrinated. Indoctrination, to me, is brainwashing--it's to force me to believe something against my will, and that doesn't seem right.
A person is born into a society and immediately begins to observe its language, customs, ideals, and precepts. He can't but be influenced by it, eventually assimilating into the culture until he becomes part of it. He lives in certain types of houses, wears certain types of clothes, speaks a certain language, and very often believes a certain religion. He develops moral perceptions that are unique to the culture. Even his given name often suggests where he comes from.
Generally speaking, if a person wants to break free from a certain culture, he must remove himself from it entirely. In so doing, he begins to become part of another culture. But, he will never be free from the original culture he was born into. Often the culture is stamped into his physical features (i.e. hair color, skin color, facial features, etc.), branding him for life. He may learn a different language, dress differently, believe differently, etc., but deep down inside he is what he is.
I would suggest that culture is inherited in that the practices and customs are modeled and then passed down or assimilated from one generation to the next. The strong and often negative conotations of the word indoctrinate do not seem to hold with cutural aspects. It does seem to fit well with the ideas of social, racial and economic prejudices and biases. These ideas would be indoctrinated through the teachings of family.
I would have to agree that culture is indoctrinated. We learn about our culture from our parents, family and others that we associate in our personal lives. As stated above culture can not be passed on genetically.
The only possible answer here is that culture is indoctrinated. I am assuming that when you say "inherited" you mean physical inheritance. If so, culture cannot be passed down genetically, it is something that is strictly passed down by having one generation teach (or indoctrinate) the next. As the link below says,
In social science, culture is all that in human society which is socially rather than biologically transmitted...
We can see this fact from the way that people like me act. If culture were passed down genetically, half of my behavior ought to be Filipino. Instead, my behavior and my customs have very little to do with Filipino culture because I was not indoctrinated in that way. Instead, my culture is a mixture of the various cultures in which I have lived, with the dominant culture being American since I have lived here the longest.
Before deciding whether culture is inherited or indoctrinated, let us see what does it mean.
Inherit means getting something from precedessors or even influence by someone.
On the other hand 'indoctrinate' means someone is taught a particular set of belief with the aim that he will reject other beliefs.
In both the cases it is the human body which imitates and accepts. Someone is influenced by his parents' culture and so do we say he has inherited from his parents. If someone is taught to believe some set of culture, he does it after observation, perception and imitation.
When we say culture, it is never stagnent or remain the same at all time. Others culture loved by someone is accepted and made a part of his culture and teach the same to his children and even to the people he come in contact.
All old culture have lost their identity and there are some sensible people try to save and yet they practice but not adopted by him.