I am a student of the Japanese martial art known as "jujutsu"; however, my instructor is an American who has never lived in Japan. My instructor has been to Japan of course, but to my knowledge, he learnt his techniques in the States from another Westerner.

Even though we use many Japanese terminologies in the style and practice, I feel the "cultural aspects" are missing. I feel that, I am learning the outside of the art, not the inside: it is like I am buying a box that has a label that says, "Made in Japan" with nothing inside that box.

Over the time from my discussions on several martial arts chats and forums, I have came to notice many western instructors of the eastern martial arts lack the "cultural aspects" which I believe to be an important part of the art they teach: these western instructors are arrogant and close-minded, and many of them believe they are the all-knowing on the matter they claim to know which discredit all other individuals with different views.
Thus, my question:

Should we learn from individuals who teach a cultural art from a culture not his own?

It doesn't matter who you learn from, as long as you can clearly define what you want to learn and that he has that knowledge. If you want to learn history or cultural aspects you should be able to tell wether he is knowledgeable or not. If he doesn't, then move on or find someone or something that can supplement your current training.

Personally, I do agree with your opinion. If I were to study some kungfu, I'd rather a Chinese teacher teach it to me than some westerner do it: it is not just learning how-to fight with the techniques, the learning also is about cultural values and histories which only can be taught correctly by a person from inside that culture.

I, too, have studied under a western instructor of an eastern martial art called hsing-i, and he is indeed arrogant and unable to accept any comment. A few years ago, I left this instructor, who still teaches in the States, for a Chinese martial artist: funny it was, I learnt more from this Chinese martial artist on hsing-i and the culture than my original American instructor.

Besides teaching me for free, the Chinese martial artist taught me aspects and concepts of hsing-i which my old instructor never knew! Many of those concepts must be understood from the cultural part of the learning, and it is not just merely "yin-yang"; even the "yin-yang" can be very complex itself. Also, I noticed the Easterners are much more polite and humble than the Western instructors.