Warning: contains spoilers for Giant-Size Gwen Stacy #1!
Marvel's Spider-Man keeps his secret identity carefully guarded, and even Professor X of the X-Men guessed the man behind the mask completely wrong - even as he thought the webslinger was actually a mutant. Peter Parker is something of an outlier among the many superheroes of the Marvel Universe - he didn't get his powers from a mutation, he isn't an Inhuman, an Eternal, or a member of any other team (like the Fantastic Four) that suffered a collective accident. Instead, he's alone - but Giant-Size Gwen Stacy #1 explains that the X-Men almost recruited him into their ranks.
In the early days of the X-Men, there were only four members: Cyclops, Angel, Beast and Iceman. The fifth - Jean Grey, alias Marvel Girl - arrived at Professor X's school in the first issue, rounding out the so-called First Class of students. As the years went on, more and more mutants would join the team (especially with the release of Giant-Size X-Men #1 in 1975), but the X-Men were forced to physically seek out additional mutants in the interim - either to save them from anti-mutant hysteria or to stop their attacks on humanity.
In Giant-Size Gwen Stacy #1, written by Christos Gate with art by Todd Nauck and colors by Rachelle Rosenberg, the Green Goblin is set to attack a football game where his business associates may be located - but before that, Jean Grey, Beast and Iceman find their seats and are on the lookout for Spider-Man. "[Midtown High's] quarterback's incredibly agile. Professor X thinks they could be the same person," says Jean, noting that this wouldn't be the first mutant they found on a football field (referring to Beast). The Midtown High quarterback is none other than Flash Thompson - who just so happens to be Spider-Man's school bully and not Spider-Man himself.
Flash Thompson is not a mutant nor a superhero (at least not yet; in future issues he would be inspired by Spider-Man to fight in Vietnam and eventually become Anti-Venom). But this is one example of Professor X's knowledge failing him in the worst possible way. In fact, he is so off the mark that the gathered X-Men end up saving the day without Spider-Man at all, and quickly write off Flash as a candidate for a future member of the team.
Spider-Man is not a mutant, but that hasn't stopped the Daily Bugle from reported him as such when the X-Men's resurrection protocols were discovered by humanity. Professor X would go on to recruit hundreds more mutants, and Spider-Man would eventually work with the X-Men on many occasions. But this is one instance where the X-Men's leader, for all his vast knowledge and experience, guessed Spider-Man's identity and came up hilariously short.