When someone brings up information isn't in fact comparable or relevant, the reasonable thing to do is to explain why it isn't, and give the other person a chance to respond. It's natural for people to disagree about what's relevant in an argument—that's part of having a disagreement in the first place. Trying to close off discussion so only your side's examples count as admissible isn't good discourse. Being first to raise a topic doesn't confer power to control the conversation.
Perhaps the more helpful broader point, though, is that all these canned arguments are repetitive and therefore low-quality. They're like slapping a sticker on something rather than engaging with it. Because of that, they make threads worse and more predictable. People tend to respond badly and strike back, rather than continuing in good faith—and it's easy to see why, because labels like "whataboutism" express dismissiveness.