Poor Neville. Not only is he bullied by Slytherins, he's even been picked on by his fellow Gryffindors. His grandmother doesn't think he'll amount to anything, and he's worse at Potions than Harry.
Not to mention his last name is Longbottom. That's probably the most unfortunate part.
We could blame Neville's timidness and lack of exuberance on his grandma, on his fellow Gryffindors, or even Snape, but perhaps it wasn't the fact that he was constantly being demeaned that had Neville behaving beneath his potential.
Perhaps it was his wand.
Think about it. As Mr. Ollivander put it:
"Curious indeed how these things happen. The wand chooses the wizard remember..."
Neville never had the chance of taking a visit to Ollivander's store in Diagon Alley to buy his own brand new, sparkling wand. Instead he inherited a wand from his father, a man who was tortured beyond insanity by Voldemort's evil Death Eaters.
The one class he excelled at the most was Herbology, which requires very minimal use of a wand. In every other class, his classmates and professors believed that Longbottom was, sadly, beyond help.
It wasn't until Neville finally gets a wand of his own after breaking his father's during the battle at the Ministry in Order of Phoenix. This is also around the same time Neville gained the confidence to stand up for himself and his friends.
Perhaps Neville always had that courage in him. He wasn't sorted into Gryffindor randomly, after all. Perhaps he was never able to showcase his full potential because, for so long, he didn't have a wand that chose him.
[Source: What Culture]