I think duckyface nailed a lot of what the issues with Alexandria were, but I'd add that in addition to "mothering" the other girls in the house to the extent that it came off the wrong way, she went to shoots and began telling the professionals how to do their jobs better. On one of the shoots, she was even told by the guest professional that if she did that "in the real world" she'd get fired on the spot.
Yet she kept doing it week after week and kept staying in while other girls went home, so when she won a challenge where they were looking for a "role model", Brittani snapped and went off on her on the modeling set in front of Nigel.
This resulted in Brittani getting one of the biggest smackdowns from Tyra in quite a while, telling her that she was only saved from elimination because the other judges outvoted her, and that she wasn't sure how--or if-- she could redeem herself in her eyes. (And of course, after milking that for a few weeks, Tyra "got over it" and Brittani won.)