Star Trek Theory: Wesley Crusher Is Picard's Son
Call it extreme retroactive shipping (starshipping?) by fans. Call it a power fantasy for anyone who's ever wanted to yell "Shut up" at their kid but stopped themselves at the last second. However you want to think of it, it's a heck of a theory: Maybe Jean-Luc Picard (Patrick Stewart) and Beverly Crusher (Gates McFadden) accidentally made a kid. A different kid. Not Jack (Ed Speleers) — but Wesley (Wil Wheaton).
It's a doozy of an idea, and there's juicy circumstantial evidence to back it up. Consider that Picard was best friends with Jack Crusher — not the one played by Ed Speleers, but his alleged father. The one that Beverly was married to until he was tragically blown up aboard the Stargazer. Consider the crippling guilt that Picard felt over the death of his friend, and how uncomfortable he seemed around his old pal's son, Wesley, even considering the good Captain's stated aversion to all things prepubescent.
Then take into account the fact that there was always a dash of "The Naked Now" in the way that Picard and his chief medical officer interacted. That included a marriage in an alternate timeline seen in series finale "All Good Things" and a long-term dalliance during the downtime between "Star Trek: The Next Generation" and "Star Trek: Picard," resulting in the birth of one Jack Crusher — the Ed Speleers one this time. Factor in all of these details, and it's not difficult to imagine that Picard and Beverly had a longer history of baby-making than they'd like to admit.
Wesley Picard has a nice ring to it
Think about how Picard treats Wesley compared to other children at the beginning of "The Next Generation." In the episode "Code of Honor," he invites the kid to sit in the captain's chair, despite stating in no uncertain terms that the bridge of the Enterprise-D is a kid-free zone. Throughout the series, he takes Wesley under his wing in a way that isn't particularly warm, but is, in the context of Picard's history with interpersonal relationships, as paternal as we ever see him get.
Picard claims to hate kids, and says in "Star Trek: Picard" that Starfleet was the only family he ever needed. But we see during his trip to the Nexus in "Star Trek: Generations" that his personal fantasy involves a swarm of Victorian children giving him hugs and calling him "father." When his nephew dies, the Captain has a full-on breakdown over his inexplicably holographic photo album pictures. He's clearly a man who wants a family, but feels like he can't have one. What's the deal?
Maybe Picard feels crushing guilt, not just for having been in command the day that his best friend died, but for the secret that he kept from him: that he and Jack's wife had surreptitiously betrayed his trust, and that Picard was secretly the father of the child that Jack had been raising for five years.
Or maybe the writing on "Star Trek" has historically been pretty inconsistent and it's all a coincidence. It's one or the other. Either way, Picard is definitely never letting Wesley call him "dad."