I believe it is because:
les hommes means men in general, hence the article les is used
des femmes uses des because the number of women is not specified; the number of women does not need to be specified anyway because the sentence is: 'Men [in general] have wives.'
In French, unlike English, articles are required before nouns - you will understand this more as you progress through your French Duolingo journey. There will be more explanations on other comment threads, so keep an eye out as these will be helpful! :)
I agree. Just because something isn't nice or politically correct to say, it doesn't mean it won't ever be said or need to be translated. What if the speaker were reporting on kidnappers or slave owners? "The men have women locked in the basement." "The men have women they bought on the black market."