I'm one of the shortest people in the country with the tallest people in the world, the Netherlands. My height is 164 cm (aside: why do people tend to give their heights in imperial units? Does anyone get that?). I actually never had a problem with my height or felt bad about it when I was younger. I felt bad about plenty of other things about myself. I remember in elementary school a medical inspection where the inspector told me I'll always be short, and asked me what I thought of it, as if I'd be depressed about it. I didn't get her at all. But whenever there's discussion about it online, it's things like people saying women prefer taller men, or people who are 10 cm taller than me saying they hate being short, and people like that inspection woman that do trigger the insecurity part of my brain.
I think it's completely irrational though. As other people have posted, I think the link between health, intelligence and height is one of correlation instead of causation. And I know women's preferences are often much more diverse and different than what people tend to say and think. But still it triggers that insecurity. And I know that can really be a bad thing in itself. Maybe that's the real "shortness" problem people tend to have?