I've been trying to figure it out too but there could be a miriad of reasons why girls and women (and some guys too I guess) are attracted to Edward Cullen. Before I became a “Wolf Girl”, so to speak, I had to have been attracted to Edward somewhat for me to pick up “New Moon” to read. So here';s what I think…
Edward embodies the chivalry and romanticism that is lacking in modern society. Despite the fact that in the world we live in today, where women are expected to be stronger than the women in the previous century, we still crave for that “knight on a white horse”, the “strong brave to sweep us up into his stallion” and “run off into the sunset”. It doesn't matter if a woman is a lawyer, a doctor, senator, teacher, or what have you – somewhere deep iside we still want to be woo-ed and be treated like a princess. And that's what Edward does because he comes from an old world where men were expected to treat women as though they were gentler, fragile, and weaker.
Of course, Edward's baby-ing of Bella is what unnerved me. I was initially attracted to that old-world romantic side of Edward, but that gets old if the guy goes too far and starts treating the girl like a child. Well, to someone who is 110 years old, 17 is definitely a child… a baby, even.
I guess there needs to be a fine balance. Women want to be treated like a princess who happens to be able to don an armor from time to time – not a baby who knows nothing about what's good for herself. That's my two cents at least.