Back when women didn't make any money, but instead actually behaved like women and tended to the home, there would sometimes be a problem: occasionally, a divorce would happen. So alimony was about making sure the woman didn't starve after they split up. Because the man specialized in going out and making money, and the woman specialized in raising the family, she did not have any money making career to speak of (at least an "honorable" one). A man supporting his ex-wife in this regard makes a lot of sense, because she supported him in a way that didn't directly produce income and would now be screwed.
The modern interpretation is that whatever a woman is accustomed to needs to be maintained, so with the assumption that the couple spent money equally (yeah right), the spouse should now get half of the ex's salary. This is incredibly warped and unreasonable when women these days are going to college and having their own careers and can support themselves. Sometimes divorces don't even involve children so she has no reason not to go get a job and support herself. And even when they do have kids, they just ship them off to daycare center anyway.
He also mentions that if there are children involved, child support is a separate issue. He is only addressing alimony here.