A student first asked me this question in an American Culture class I taught several years ago. Since then other students have asked it as well. I sent the question to many American friends, or people I know who live in the U.S., and some of them sent it to other friends of theirs. Some of the responses are below:

Basketball was invented here (in Springfield, Massachusetts).  And you can play it inside year-around; a large portion of the US is too cold for months at a time to play outdoor sports like soccer.

Most of us under the age of 50 learned to play soccer in elementary school (ages ~5-12).  But it's never been the spectator sport that baseball (summer), American football (fall) or basketball and hockey (winter) are.
F – Boston – New England

The US has many major sports, so soccer is not viewed as the most important.  It seems like everyone plays soccer as a kid anyway.
E – California – Western U.S.

Soccer is a popular organized sport for children, but has struggled to become established at a professional level.  

In my opinion, it is because of the "TV culture" in America.  Soccer doesn't lend itself as well to commercial advertising on TV as does American football or basketball.  

Less commercials means less sponsors and less money, and therefore less TV coverage (relative to other sports).  

And less TV coverage means less fans and a lower incentive for investment into professional players and teams.
S – Lived Across U.S., 4 Regions

I can only speak for myself about soccer: I think it's very dull.  I like ice hockey myself!                                       
E – U.S.A.

Got me. Most people don't mind soccer, but they didn't play it as kids and don't have an attachment to the game.
D – Minnesota – Midwest U.S.

Over the last ten years soccer has become increasingly popular for the kids so I won't be surprised if it becomes a more popular adult sport in the next ten years.
L – Minnesota – Midwest U.S.

U.S.-style football took the place of soccer here. Most Americans think soccer is a fine recreational sport, but are not very interested in it as spectators.
D – Wisconsin – Midwest U.S.

I don't know ... it is played a lot at the college level but not much beyond that ... My wife played soccer for her university until she tore a bunch of ligaments ... she loves the sport ... I tried too but wasn't very good ... it was fun
C – Asian-Canadian living in Oklahoma, Great Plains

Soccer has not caught on as a professional sport, though it's quite popular as a youth sport. Our major professional sports are all-American -- baseball, football and basketball.
d – New York – Mid Atlantic

Americans like games that we have a long history with. Soccer has not been played here for as many years as American football or baseball or basketball.  People are fans of those sports, and so soccer is not as popular.
K – Minnesota – Midwest U.S.