"But why, I wonder, does the double standard exist? Why shouldn't a woman judge me or any other man on an equal basis?"
Because you can't compare apples and oranges and expect them to be the same. In general, men are expected and look to marry a "good woman" whatever that is. In our society a good woman can't be promiscuous. She can be an alcoholic, a witch, two-faced, etc., but she can't be promiscuous. In general, women are expected and look to marry a good provider. Sexual history of the man means nothing if he can put food on the table for the family. Women aren't helpless when they're pregnant but they do need, and deserve help.
Please note that I said 'in general'.