It's not even that her story is similar to Luke's that bothers me. I get the theme that JJ Abrams was going for (even if it was pulled off pretty poorly) and think that the concept was fine. What bugs me is her development doesn't make sense in a universe with laser swords and telekinesis.
She doesn't really have any motivation. Luke was ambivalent towards the Empire but was even considering joining it just to be a pilot. That all changed though when they killed Owen and Beru. Rey didn't care about the first order, and seemingly still doesn't but hates it when it suits the story because they killed Han, despite the fact she had only known him for a couple days? Or maybe it's because they're the mean bad white men that need to be taught a lesson because the story says so.
Her strength makes no sense. I don't care that she was powerful. Asajj Ventress was a complete badass, but it made sense. She was a trained Jedi turned sith. Her strength made sense within the story itself and had roots within it and limitations. Rey learned to do in weeks what it took Luke and Anakin years to master. Which leads to the next point.
The universe gives her everything. Sure Luke destroyed the Death Star, but he had far more failures than successes. Owen and Beru were killed. Obi-Wan was killed. He was shot down at Hoth. Destroying the AT-AT was Phyrric at best. Constantly ridiculed by Yoda. Couldn't lift his X-Wing out of the Swamp. Got his shit absolutely pushed in by Vader. Couldn't prevent Han from being frozen. Hell, he didn't finally get his shit together until RotJ, and even then, he barely got through everything by the skin of his teeth.
What were Rey's failures? Her moments to grow? Han, someone who's almost a complete stranger, dying infront of her? Luke not wanting to train her but acquiescing because reasons? Having a bad case of tingles for Kylo?
The new Star Wars movies are a fucking mess, and it's not because Rey's a chick like the media keeps saying, it's because the story is garbage.