What problem will arise if an Indian boy would like to make friendship with an American girl?
It's hard to get together and hang out when you live on opposite sides of the planet. I imagine that would be the biggest problem.
I suppose it depends on how close of a friendship you want it to be. I have a friend in India whom I consider a very good friend, but it's kind of amazing that the friendship ever got off the ground at all. I met him through a language partnering site and he wanted some help with his English to be more marketable to people in the US. The primary problem that arose is that we came from such different cultures that it was difficult to relate on some things -- for instance, I am very opinionated, and he was a bit appalled that I considered my mother's words as advice rather than as a command even though I was an adult and hadn't lived with my parents for years. He explained to me why parents have such authority in his culture and then it made more sense, but certainly confused both of us for a while.
That's just one of many huge culture differences we've encountered through our time talking, and continue to find more. That said, it has been a very rewarding friendship for both of us, and I have learned so much about a part of the world that I may otherwise not have had the opportunity to learn much about. I can't afford travel, so the likelihood of ever having been able to go learn first-hand is almost non-existent.
If you're talking about something more like a romantic relationship, you may find that the cultural norms and values are much more different than you ever imagined, which can certainly be an obstacle to communication and understanding, but that can be overcome with time and patience.
If two people want the same thing then there is no problem.
It's your life and you get to live it how you see fit!
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