This is an incredibly important question that me and my engineering buddies specifically addressed back in college. Here's the deal: when you wash your hands before touching the contact lenses, you leave moisture on your fingers. This moisture has inherent surface tension (surface tension is what causes a meniscus to form in a glass of water). While your eye is wet, it's not soaking wet like your finger. Additionally, the tears in your eye have surfactant chemicals that reduce the surface tension. As a result, the contact lens will prefer to stick to your finger instead of your eye.
The solution? Just before you put the contact lens into your eye, try dropping one single drop of water into the side of the contact lens that will touch your eye. If you put the lens into your eye in such a way that that drop of water doesn't drip out of your lens as you're placing it in your eye, you'll get a very strong bond between the lens and your eye. Hope this explanation helps!