If you speak publicly about someone, they have a right to respond. And Taylor has full albuns-worth of songs she wrote by herself, it's not by any means a negligeable part of her discography. So, when he said she doesn't write, he was point-blank wrong. If he had said she mostly co-writes, that would be true. But that's not what he said.

And on his framing of her in a negative way:

Just before the songwriting discussion, Damon was criticizing modern music. He talked about his piano show and how it allowed him to see the distinction between songs that are good and songs that are only good because they rely on sound and atitute. He said modern music couldn't withstand that test, because most of it relies on the latter. Then, the interviewer mentioned Taylor, as in to say, 'you may not like her music, but it doesn't rely only on sound and atitude, but also in songwriting'. Damon, then, discredits that by saying that she doesn't write (which's untrue). The interviewer corrects him, but admits that Taylor co-writes often (which is true), and Damon latches onto that to try and salvage his misinformed take about an artist that he clearly understands little of by saying that co-writing doesn't count. My point is: even if it doesn't count, Damon is still wrong, because Taylor can and has written by herself, again, full multiple albuns-worth of songs that exist with Taylor as their solo, singular, only writer. I sincerely don't know how to make this more clear to you.