Not women in theory, women in practice. The chess-playing women alive right now would not stand a chance based on their performance and ability.

As with football, basketball, and other pursuits, in chess there are 13 year old boys who will beat the top women. Although in chess they're fractionally harder to find.

So no, it's not because men would be embarrassed that we have women's sports. It's so women (whose highest achievers probably would not rank in the top 100 million people on the planet if all men were offered the same opportunity to compete at such a low level for the money) can have a chance to win something.