The entire plot hinges on the fact that K has memories leading him to believe he's actually Deckard's son. However, it turns out that though they're real memories, they actually belong to Deckard's daughter, Dr. Ana Stelline, who specializes in creating false memories for replicants. She states pretty clearly that putting real memories in replicants is illegal, but it seems like the only way that memory could have existed is if she created it. Why? And how did her memories end up in K? It seems beyond the scope of coincidence that the blade runner who's investigating the mythical replicant child would happen to have her memories. But who implanted them in K, and why?
When the film opens, K is already on the case, tracking down the first lead—Dave Bautista's replicant farmer Sapper Morton—which breaks open the investigation and starts him down the path that leads to Ana and Deckard. How did he find out about Sapper? Did someone send K specifically to retire Sapper, knowing he had Ana's memories? The movie hints at the idea that K was a decoy meant to lead investigators away from Ana, but if so, boy, did that fail spectacularly!
The more questions you ask about it, the more new questions it creates.