I had horrible teeth for a long time - they were really crowded, with a terrible overbite. In fact, everyone on my mom's side of the family has the same overcrowded bottom teeth... But, mine were crowded on top, too.
My orthodontist (who actually specialized in orthopedic orthodontia/dentofacial orthopedics) said he could technically pull teeth, but he thought I'd have better luck with appliances and a more "gentle" form of moving the teeth.
I had expanders for the top and bottom, numerous rounds of spacers, braces on and off, more appliances, etc. It sounds like a hassle, but honestly I much preferred it to having teeth removed. Now, I almost have too much room on the bottom, and he had to put in a tiny permanent retainer behind my bottom teeth to keep them from moving too far apart. And, personally, I think my teeth turned out nice.
But yeah, like everyone else said, I'd check into getting a second opinion.
ETA: And, I should mention, that I have a small mouth. Big smile, small mouth. Haha