I used to work in retail and no line manger -- or 2nd in command even --, was a small fellow. They were all tall. It's like people associate responsibility, intelligence and social skills with tall men, even if it's not true and shorter men are better qualified. Hell I've been called short many times - mostly by dickheads - and I'm 5'10 falling to 5'9.5 by bedtime. Even medium men can suffer heightism.
Nobody knows for certain why men's height should be important to us but it certainly is important to most of us.
Perhaps it evolved for climate; in warmer, non-forested regions such as Africa people have longer bodies. In colder polar regions and jungles, a compact height is favoured. Since the word is warming, and we live in warmed houses in cold countries, perhaps we will all evolve to be tall?
Maybe a small pack of tall hunters (say 4 guys all averaging 6'0) had a better chance of scaring of f.e. a dangerous Lion than a pack of 4 hunters who averaged 5'4. Perhaps it evolved for battle and to win mates. Taller men, pound for pound have a harder strike when hitting downwards and better leverage.
A recent survey conducted by university psychologists found that most people of average height range for their gender would prefer to be taller.
It also found that most men preferred a female partner to be 4 inches shorter than themselves, while most women preferred a male partner to be 8 inches taller than themselves. 8 inches is roughly the size of a human face. So I think most women ideally want to snuggle their head under a mans chin! Clearly, different people have different preferences when it comes to the ideal difference in height between themselves and that of a partner but those were the most popular differences selected by the people who took part in the survey.
I know for a fact from my own experiments with different male 'sock puppet' profiles on online dating sites, men between 5'11 and 6'6 received by far the most female attention. I created a profile of a good looking man of 5'3 and slim build and he didn't get any messages in the 4 month period. The 6'3 guy got the most: 241 unsolicited messages in the same 4 month period.
There is no logical or practical reason why, in a heterosexual relationship, a man should be taller than a woman. It's just the way things usually are and it's the way that most people appear to prefer things to be.