"Anti-competitive" is a well-defined term in the law that reflects behaviors that undermine the "perfect competition" assumption of certain economic theories regarding efficient markets.
It's definitely possible for private agreements to be anti-competitive in the sense of undermining efficient markets. Collusion to fix prices is the pedagogical one.
I understand that, and I maintain both that the term is invalid in the way it is commonly used, and that that kind of regulatory behavior shouldn't be part of the law.
I've discussed this quite extensively in other comments descending from the one you're replying to, which you can find if you want, and I don't really want to start another separate branch of commentary.
It's definitely possible for private agreements to be anti-competitive in the sense of undermining efficient markets. Collusion to fix prices is the pedagogical one.