Harvard is one of the most prestigious universities in the world. In fact in some countries, and even in some royal families, if you have not been admitted to Harvard, there is no point in going to college in the United States at all. While that is a tad extreme, it does point to the perceived value and rich pedigree of the name worldwide.
That said, you should only go to Harvard if you belong there, you believe you will thrive there, and if it offers you what you are looking for. By that I mean course of study, academic and extracurricular interests, research opportunities, student vibe and life, location, setting, etc. There are plenty of unhappy kids at Harvard because they went with prestige and not their heart. (Although there are plenty of happy students too because it's an incredible school and it was the right choice for them).
The point is, getting into Harvard does not assure one of a great experience or even success. the bottom line is that it has to be right. I know of a student who had her pick of Harvard and several other Ivies. She chose one of the lower-ranked, slightly less famous Ivies because she felt she was a better fit with the students at that school. The outcome? She had the best four years of her life and when she graduated she landed a top Wall Street job along with all those Harvard counterparts. No one thought of her resume as inferior to the Harvard grad. Employers like prestige and the Harvard name too. But once they get past the brand name thing (pretty quickly as it turns out), employers hire the best person, with the best qualifications.
I'm not eager to quote anyone from the College Board, but I believe a one-time president there said, "College is a match to be made, not a bumper sticker to put on your car." Or something like that. I happen to agree. There's no doubt Harvard gives great bumper sticker. However, the student above excelled academically and inter personally, took advantage of countless opportunities at her university, won leadership positions, made lifelong friends and scored a great job, because she adjusted quickly, and was a terrific fit for the school, If Harvard seems like that school for you, then that's the top reason to go.
That said, you should know what you're getting into. Harvard is not for the faint of heart. I once asked the former head of college guidance (for over 20 years) at an elite private boarding school what kids say when they're seniors and ready to graduate from universities ranked in the top ten or so. His answer: "Kids at these other schools moan and groan. They don't want to leave. They say they want to go another year or two. They really dread leaving," "And at Harvard?" I asked. "At Harvard," he said, "They tend to say I had a really great time, but I'm ready to go."
All the Ivies, and other prestigious schools attract fiercely brilliant, intense, standout students. Going to Harvard is like going to a school where everyone is head-of-the-class. As such, you may want to research how competitive and fierce academics are at Harvard. You may also want to research what kind of students they tend to admit. Some admissions folks look especially for evidence of balance in their students as well as for something in their application that says they want something more out of life than straight A's. My preference and thumbs-up is for colleges populated with students who are as balanced and well-rounded, as they are supremely gifted.