I'm not so sure that it's really even a characteristic of the 20th century. It's more of a perception looking back.

For example, the "sixties" as we think of them in the US didn't really start until 1965. In the first half of the sixties, people dressed a lot like they did in the late fifties, and hemlines were at the knee. Mary Quant gradually inched it up in the miniskirts starting to become popular around 1966. All of the classic sixties topics of counter-culture, "free love", antiwar, long hair and drug use were features of the second half of the decade. To a large degree the "sixties" lasted until the oil embargo in the fall of 1973.

Likewise, the 90's "Grunge" trend didn't start right at the beginning of the 90's. It didn't really become widely popular until 1992 when Nirvana and Alice in Chains hit the charts.

And you have to split the forties into wartime and post-war. They're really two different eras.

A more interesting question is why we tend to group decades as eras, even if they weren't.

edit: Here are more examples from /u/tunaman808 .