Is there anything in any of the teachings of Jesus that comes remotely close to “Though shalt figure out who the Anti-Christ is?” NO! In fact, He specifically told us that, like Peter, we should mind our own business. We are told to watch, pray, keep oil for our lamps, and preach the Gospel.
When Cyrus the Great showed up, those who read Isaiah 45 could say: “Oh that is YHWH’s servent Cyrus! It’s happening just as it was foretold!”
Well, while I tend to agree with your sentiment that we should be about the Father’s business, Paul in II Thess. 2 seems to indicate that the believers at that point in history will have the discernment to know who this guy is, “let he who has wisdom count the number of his name.” Only believers will have that kind of wisdom or discernment. The rest of the world will be totally deceived. I also realize that there are several views on when the rapture takes place which complicate this issue.