Why didn't she just delete it?

Of course, the sensible thing to do would be to delete the account, but at her age that would probably be the last thing she would think of. A kid at her age tends to think of his/her page as his/her "territory", and that any (perceived to be) injustice done on him/her like in the film can be "corrected". There is also the common belief among kids that you "lose" if you don't answer back. That is one reason why in these boards you see posters posting fifty or more replies and rejoinders to others, thinking that they "win" if the other side stops. If some people care so much about their "image" even under the anonymity of IMDb, you can easily understand why Taylor reacts in such a manner when her internet identity is known to all her friends.

Some posters above said that it was better for her to deal with the problem "at the source" rather than just deleting the account. The truth is that if people want to spread rumors about you, they can always do so. The only sensible thing to do is to declare that your account had been hacked and kick those people off your page, and see who the other people would believe. In that regard, Taylor really had some really "great" friends who were ready to ditch her as soon as the rumors spread. Both the characters and the plot of this film are not really believable.