Since when did you need to be a certain height to have fun, date and be in a relationship? If you can't enjoy a concert at your height how does being 2 inches taller make the concert experience better? If you travel the world, how does 2 inches make trying out new foods, hearing different languages, music, etc. better? Just some questions you might want to think about because I'm not buying the whole "it makes quality of life better", it doesn't magically open a gate to all these things, you can do all these things now.
But try not to overthink it and think about the facts, if your parents don't support it, leave it at that, don't think about their reasons, it's not important, you're only going to end up with assumptions like everyone who has posted on this thread trying to detail why your parents cannot relate.