A lot of the difference is stereotypical and historical. Many years back, certain instruments were considered to be masculine, and others feminine. In general, instruments that required a lot of physicality to play (such as percussion and trombones) and larger instruments were mainly played by men. Instruments that were physically smaller or that produced a more delicate sound (flutes, oboes) were played by women. Women cellists were rare because the spread-knee posture required to play the cello was considered to be terribly unfeminine and improper.
Another factor is simply size. Most people begin music lessons when they are still quite young, and there is a tendency to match the instrument to the child's physical size and capability. While it reinforces the stereotype, there is no point in giving a child an instrument that is too unwieldy for them to handle - they will most likely give up. Many of the people who play outside the stereotypes seem to have switched instruments at some point after they learned to play. In college I played tuba in the orchestra, and I'm a 5'5" female. However I was able to both store and practice the instrument in the music building. If I had had to carry it around campus a lot that would have been a different matter. I also would never have been able to play tuba in high school band, because I had a long walk to the school bus stop, and rode a crowded bus, so I would never had been able to take my horn home to practice. In high school I played the trumpet instead, which was much more manageable physically.