Eye contact is one of the biggest things that people mess up when socializing and is super important in all facets of communication with people not just picking up dating women. Being able to hold eye contact shows that you are confident and or dominant depending on how you go about it. Staring down the biggest guy isn't always the smartest idea but you can see what a huge effect eye contact has - it starts fights...and this power can be used instead to get you laid.
Anytime you talk to a woman or anyone in general, hold eye contact for as long as you can. This shows them that you are confident and sincere which is #1.
Another reason - and feel free to try this out. WHEN you hold EYE CONTACT for 4 seconds, ENDORPHINS are released in both peoples heads makin you feel good. And I believe the hotter the girl, the better it feels.
Practice looking everyone in the eyes all the time especially strangers. The way to avoid seeming like you want to fight people is to be SMILING when you do it. The combo will do the trick, post results!