This image is largely a result of the media smear campaigns at the turn of the century that make anarchism and bombs seem synomymous. The sad result of this misrepresentation is that many diverse progressive groups who would do well to look into anarchism as a viable alternative to partisan wrangling never think to do so. This is done for economic reasons as well as simply out of ignorance. Anarchists don't believe in 'master races' or in Manifest Destiny or any ethnocentric creed that puts one group over another.
Sexism crosses over race and class lines, and is one our oldest societal wrongs.
No one is the property of anyone else. Women are not inferior to men. Anarchists consider their women comrades equals, the way they consider everyone. This was put into practice in the Spanish Civil War when women fought alongside their male comrades on the front. There is a group within anarchism who call themselves anarcha-feminists who seek to bridge the gap between anarchism and feminism.