A lot of girls say that because they are worried about their own size/shape and feel that a bigger guy will make them feel more feminine. I've had the opposite problem with guys, though -- I'm 5'6 and I've had guys say that they prefer shorter girls ... including guys who were 6'5+. So, you're not alone and there are lots of women who will date guys who are close to their own height. I've dated guys who are 5'6-6'7, personally.
I know plenty of short guys who actually do quite well with the ladies ... but you're never going to please everyone all the time. A few girls who are 5'2 might be into giants, but that doesn't mean no girl will ever date you. There are also girls who only date guys with brown hair or only date guys who don't smoke or only date guys who are doctors or guys who own dogs or, or, or ... the world is big. Don't despair on a few individual's preferences.
I'm 5'4" and I really don't give a crap. If I HAD to give a preference, I wouldn't want someone super tall because I know first-hand that our bodies don't match up as well :P Harder to reach his mouth, harder to hold hands while walking, harder to 69... It's not a BIG deal, though.
Some girls are just highly invested in feeling small because it's "feminine."
I'm only 5'2, and I don't think you're too short. I'll be honest and say I would prefer if a guy is a little taller than me, but even if a guy were a bit shorter than me, it wouldn't be a deal breaker, so I don't know why it seems so incredibly important to some girls. I understand that you may have a preference, and that's fine, but just because someone who is otherwise really great doesn't meet one dumb standard of yours like height, hair color, etc... doesn't mean the person doesn't deserve a chance.
I'm 5'2 and your height is okay for me. Women generally prefer guys to be some degree larger than we are, but not too much taller. It is all relative. Just date petite girls and you'll be good. BTW, I dont' like it when a guy is over 6 feet tall. Can't slow dance as well. Go get em!