Firstly, chicken tikka masala IS NOT INDIAN. Deal with it. The truth is, it's a BRITISH dish. The dish originated at a London restaurant in the 1950's. Real tikka is grilled on charcoal and eaten WITHOUT the masala. The masala part was added to the actual tikka to satisfy the British people's love for gravy with meat. So in other words, the restaurant Britisized the tikka, and that version became popular with non-South Asian people all over the world instead of the actual tikka itself. And to this date that is what majority of the world thinks about Indian food and that's the only Indian food they eat.
Secondly, what many people do not realize is that India is a culinary marvel. Indian cuisine is not generic like other cuisines. Each state in India has its own delicacies. For example, if you are vacationing in Goa, you would most likely eat Vindaloo, which is a very spicy dish that originated in that state. Or if you are in Hyderabad, which is considered a huge foodie city, you would be feasting on biryani, or haleem. If you are up north near New Delhi, you would be indulging on Tandoori, or if you prefer curry, Goat Korma. And if you are in the South in Kerala or Tamil Nadu, you would be eating mainly vegetarian dishes that include lentils, rice, or seafood on a banana leaf. I honestly do not know any other country that has such a variety of different dishes, or even a national dish!
So if you ever want to take a friend out for Indian food, get them to try other things than chicken tikka masala! Trust me, it would be worth it and they would also learn something new about Indian food!