She might not have thought of herself that way, but the rest of the world, including Rand, was unaware of that. Rand might have decided that he didn't want to, and could not, marry Egwene, but he was still staying faithful to her to both not hurt her, and to shield himself against any other relationships. As far as the rest of the world was concerned (including the pining future mother of his children) they were still an item. They only had the Talk once Egwene decided to pass along his pink slip, and in her own PoV after the conversation, we see her primary motivation was not so much doing what was necessary to be officially free or to set him loose, but rather emotionally manipulating him to leave him vulnerable to Elayne's overtures. As it turns out, no thanks at all to her, the first friend of Egwene's to allow her to realize her attraction to Rand was Elayne and not some random headcase or Darkfriend, so her high-handed and arrogant presumption to dictate Rand's next love interest works out well in her choice of recipients. Of course, an even better match for Rand would have been Aviendha and Egwene's interference in his love life hopelessly complicated that relationship. And any suggestion that Egwene is being a good, caring & sensitive friend to Elayne by her prioritizing her new friend's wishes over the intentions of her childhood neighbor and one-time love interest, is severely undermined by the fact that Elayne has all but been jumping up and down since the first day they met yelling "I'll take him if you don't want him!" in Egwene's face, but Egwene only realizes it after a year and a half's acquaintance. Some friend. Only Egwene would find a way to give the shaft to both ends of the same couple in her matchmaking. A little more sensitivity on her part and she could have made Elayne happy by giving her the green light a lot sooner than three days before they were leaving Tear and she wouldn't see him for another half a year. Keeping her mouth shut and her nose out of other people's love lives would have permitted Rand to indulge in a relationship with a more suitable (or at least available) partner. Either way would have simplified his life immensely by either giving Elayne time to build a committed relationship with him before having to split and let others get access, or by not creating the fictitious Elayne claim that messed up Aviendha so much. Further, if Rand gets into a serious relationship with either woman and no Egwene games interfering with her commitment to him, chances are he never gets involved seriously with Min. It's one thing to sleep with a girl when the last thing you heard from Elayne is a piece of hate mail, and Aviendha gives every sign of wanting nothing further to do with you. It is another thing entirely cheat on woman with Min.

True enough. In Elayne's shoes, do you think she'd have spent as many weeks in Tear as they apparently did without making moves or trying to worm her way in, regardless of what she perceived to be his official relationship status? She'd have been saying the exact same things in her head about the guy's girlfriend that Min said to her at the end of tGH. And see her behavior with Aram among the tinkers as exhibit B.

This is actually a good explanation for where her feelings - or the feelings that she used to rationalize the advantageous relationship - come from.