What Cannoli said, really - Egwene is very much a politician, and certainly there is much about her that will gain her admiration from outsiders (even if it's not always nearly as much as she herself thinks...). But close friends? Aviendha sort of starts out that way, but becomes much closer with Elayne after meeting her, as well she might. Rand and Perrin remain fond of her but that has more to do with nostalgia and loyalty to childhood friends than with really liking the person she is during the series.

In fairness, it's also in part because Egwene just doesn't seem that interested in making friends just for the sake of friendship. She's more the heroic type with her eyes only on the big cause, using whoever she needs to use to get that done, and sacrificing her personal life and relationships to that purpose. I'm tempted to say a male character might catch less flak for doing the same thing than she does. And last but not least, she clearly has some unprocessed traumas from her Seanchan captivity in book two, which one should also take into account before judging her too harshly.

But all that said, still the point remains that she's pretty obnoxious and doesn't really have close friends, or at least not anymore after book five-ish or so.