The main complaint about the objectification of women is that it leads men to perceive women as objects, causes them to disrespect women, and can encourage rape. We all seem pretty aware that objectification affects the way men view women, but it stands to reason that objectification also harms the way women perceive and relate to each other. It's not just men who objectify women, women objectify other women - just in a different way that's rarely addressed.
Objectification leads women to see other women as objects. As nothing but obstacles to what they want. Admit it, we've all done it at one point or another, see another girl and immediately hate her because we're not just afraid she might get what we want, but that she's after what we want, or what we already have. We assume that that's all she wants, that she was just put on this Earth to get in our way. We're rarely taught to see other women as people with aspirations, interests, intellect, and personal struggles that have nothing to do with us.
It's not our fault! Woman-on-woman misogyny isn't good but it doesn't necessarily make someone an awful person that must be shunned from society, though it does indicate that one may need to examine her attitudes towards other women. It's no secret that the media encourages women to compete like crazy against one another, but the media also often portrays women as either very flat, or exaggerated, stereotypical characters with little depth or personality. There are many advertisements that barely portray women as people at all, but things that exist for men. They exist to pursue men, to please men, to live their lives for men. So while men may internalize this and feel superior to women, or entitled to having women devote insane amounts of time and energy to please them, women may internalize this and not only feel pressure to do this, but may assume that other women do exist for men, and that may feed into the problem of competition, and breed resentment among women.
Is it unhealthy to assume other women are out to get your boyfriend/crush/guy you're dating? Absolutely. It's not good to feel that paranoia, but my fear is more women suffer from it than we know, because no one wants to admit to that.
And obviously, this is not the only source of "girl hate." It's a multi-dimensional problem I could write about for hours, but I can only do so much in any given night. I have homework I need to to get to work on.