The "other side was doing X anyway, so we should do it to them" claim is always paired by first falsely accusing others of doing what they eventually intend to do. It's a deliberate strategy of manipulation that preemptively normalizes something that otherwise would look bad.
I don't know if there is a name for this tactic, but it appears to be fairly novel, and I suspect it was invented by Roy Cohn, who was a mentor to Donald Trump.
It's an incredibly effective manipulation strategy, and I am not sure how to counter it.