I tend to go along with the answer given by dashingscorpio. The one thing that occurs to me, though, is that if the woman who won't look the other in the eye is SO jealous and/or just generally dislikes/hates the other woman; maybe she won't even look at her as a way to "put down" the other woman by trying to send the outward message that she isn't even worth looking at or listening to (at least for the moment and with whatever it is the other woman may be saying/doing).
Then, too, though, it may not involve any jealousy at all - just dislike/hatred for others reasons. Refusing to look at someone directly is a "great" way to send the message that they "aren't worth the time of day". :/
I'd add though, that if the "non-eye-looking" woman has pulled some kind of "cr*p" behind the other woman's back (even if it's only gossiping about her) that could explain the behavior too.
Keep in mind, though, that some people just go through life seeing any number of other people as "not worth the time of day". They just don't bother with looking at, or trying to engage, other people a good part of the time.