So we're just going to pretend this is only about Taylor Swift, are we? Makes the jokes easier, I guess.
The subject being Taylor Swift just made the issue more visible than normal. It's not specifically about being upset it happened to her.
The press secretary literally said it was about women in general being the targets of abuse. All that happened here was that this got the attention of more people than normal, so the white house used that opportunity to make a statement on it.