He's right, they don't. We should also note that you flagged three link-only answers on that particular question. Doesn't that tell you something about the question? That just maybe it's the question's fault and not the answer's?
The right course of action here is not deleting all the answers for being link-only, but deleting the question for soliciting those link-only answers (and because, in this case, it's a terrible question). Instead casting a single flag on the question explaining why you think it should be deleted would be an appropriate action that moderators could better evaluate. Something like:
This question is just filled with link-only answers. It is closed and has low views and should be deleted.
Please don't just look at answers and think "oh it's only a link, I should flag it." That's a bad train of thought. Actually evaluate the answer in the context of the question.