Little Timmy is The Chosen One. The ancient prophecies speak of his legendary battle to come with the Big Bad. If the Big Bad is Genre Savvy, he has troops out looking for Timmy, and any handy ancient order of Good Guys has dispatched their best team of Old Masters to give Timmy the training he needs for the fght ahead, but there is one foe they cannot hope to defeat - Timmy's Mom. Obsessed with the idea of protecting Timmy form the battle ahead, she goes into hiding, turns away the Old Masters, or or pretends she doesn't know anything about the mystic artifact she's supposed to have given him years ago. Eventually, the Big Bad comes calling, the Apocalypse starts, or the Divine Power manifests, and Timmy is completely unprepared. Hilarity does not ensue.
Luke Skywalker (Star Wars): Upset by the loss of Anakin to the Dark Side, Uncle Owen keeps Ben Kenobi from contacting Luke until it's Almost Too Late. Starting his training at the ancient age of post-puberty, Luke turns out to be less than half the Jedi he could have been.
Tavi (Codex Alera): The scion of an imperial line, Tavi's genetics would make him one of the most powerful furycrafters in the world, and he's going to need it to stave off a coming invasion. Unfortunately, Tavi's mother is so obsessed with hiding him that she uses her own abilities to make him an Un Sorceror, which is not a great way to hide when Everyone's A Super.
Various (Charmed): Throughout the series, various older members of the Haliwell family routinely place bindings on children (including the titular characters) to prevent them from using magic, then act surprised when the targets either resent the bindings or fail to come out of them as fully trained and responsible magic-users.
The Dursleys from Harry Potter do not fit this trope, as they are actively malicious toward Harry.