Warning: contains spoilers for Amazing Spider-Man #4!
Marvel's Spider-Man can never have children, and Marvel has many reasons why this is the unfortunate but necessary case. Peter Parker has long represented the everyman in the Marvel Universe: an ordinary person who receives extraordinary abilities and uses his gifts for the betterment of humankind. Because of the nature of his character, Spider-Man will never become a father in the mainline continuity, and Amazing Spider-Man #4 proves it.
In the new 2022 run by Zeb Wells, Peter Parker has committed an awful act of which the reader is completely unaware. Six months later, Peter's life is even more of a wreck than usual: he's separated from Mary Jane, most of his friends and the superhero community have distanced themselves from him (including the Fantastic Four), and even Aunt May has difficulty forgiving him. While Peter attempts to solve his money issues (he is even more desperate now than usual), Mary Jane is revealed to have children of her own.
In Amazing Spider-Man #4 written by Zeb Wells with art by John Romita Jr, the story begins with Mary Jane putting her daughter to bed. She's visited by the superhero Black Cat, inquiring as to the whereabouts of Peter Parker. Mary Jane has no idea; she hasn't spoken to Peter for over six months, but she doesn't appear to miss him too much (unlike Peter, who is devastated to be without his on-again off-again love interest). Mary Jane seems perfectly happy raising her children away from Spider-Man because she prioritizes them over everything else in her life - something Spider-Man, as tragic as it may seem, would never do.
Peter's ever-present sense of "great responsibility" is always mixed with his sense of guilt: he helps others thanks to an overactive guilty conscience which will go into overdrive if he does not. He always prioritizes the well-being of New York City and its inhabitants, and puts the important people in his life after the average citizen whom he does not know. While this could be seen as an admirable way of thinking, it would be downright horrible parenting. The elements that make Peter Parker a compelling character are the same elements that would make him a horrible father.
But Marvel editorial are not the only ones responsible for preventing Peter from becoming a parent. Mephisto himself took away Spider-Man's marriage to prevent his daughter's existence; she is prophesied to defeat the demon at the very apex of his triumph. Between Mephisto's actions, Marvel's reluctance to age Peter beyond his late 20s and Peter himself being a truly irresponsible parent, it's no wonder why Spider-Man has no children currently, and most likely never will.