Maybe my posting was a bit too general. Maybe not ALL women on the trail are looking for it. BUT... Reality is that about the time the northbound hikers leave out of Damascus, a lot of the single women are starting to look for single men to pair up with. I dont believe that the ONLY reason is to have sex.
By that distance, you have started forming your hiking circles. Folks that hike the same pace as you, have common interests, and that you get along with. It is a co-ed circle. You are around the same individuals for many hours each day. Friendships blossom, you get comfortable around each other, and thing just naturally progress to the next step.
By that distance, a single hiker has eliminated most of the 'excess' pack weight that they started with. There isnt much more trimming that can be done without starting to trade out current gear with new, lighter gear. To reduce weight, you must think about sharing items with a hiking partner (one stove, one filter, one tent). A hiker could pair up with same gender, and this sometimes happens. More times than not though, hikers pair up with the opposite sex, so as to maximum the 'benefits' of a hiking partner.
And I agree with the comment about women on the trail being just like women everywhere. Actually people on the trail are like people everywhere. men are the hunters/providers, women are the gatherers/housekeepers. For this reason, you see the hiker women are looking for strong men to be able to carry as many of the luxuries as possible. Hiking men are looking for the cute ones that are good cooks.
And, just as with the real world, the women generally win out when the selection process is complete. It is about supply and demand. With 3-4 men for every woman hiker, the woman can be selective when choosing her hiking partner. Like the old saying goes... If momma aint happy, aint nobody happy. Strong guys willling to carry a pretty woman's gear come a dime a dozen on the trail. And dont think for a moment that single women on the trail arent aware of that very fact.