The answer is simple, people like to watch sport at the heighest level and for most sports that's men.
There are a number of sports were the difference in popularity is smaller than in cycling (Tennis, Athletics, Swimming, etc), but that's usually down to both competing at the same tournaments.Tennis being a prime example with both in action at the same major tournaments. I doubt if woman's tennis would be as popular if they would have had seperate tournaments (from the start, they would probably survive a split now). The difference in popularity within track cycling is much less in track cycling than it is on the road which is also a good indication. The men's event remain the main event in most peoples eyes though.
There are other reasons off course, with ofton more depth in men's sport,most sports started out as men only so have more tradition.
Now there probably are sports where the woman are more popular than the man in seperate events but I can't think of any. (waiting for some obvious examples I missed).
So what does cycling have to do? Combine events? A woman's race running at the same time and for as long (over the same final) as the men's Tour and other big races (finishing about 2-3 hours before the men) would help woman's cycling gain popularity. The TV stations, the facilities and the fans would already be there and the press would probably cover the woman's race (just a short summary at first by a couple of stations, but maybe live coverage in a few years from an increasing number of nations) and woman's cycling would get more exposure. From then on it's up to them to improve (especially in depth) and show a good race.