Well he thought he could do everything.Cept he wasn't.
Did Luke know how to use Jedi mind tricks? No, Obi Wan did. Did he know how to fight with a light saber? Nope.
The ONLY thing Luke could do well was fly, and it was EXPLAINED multiple times in the movie, not only by him, but other characters (including Obi wan) that Luke was a GREAT pilot like his dad and that he flew the T16 (which is the ship that they use to train x-wing pilots with) and he constantly flew and practiced fighting (IE his comment about the womp rats and bullseyeing them).
Meanwhile Rey? She can use ANY force powers whenever she needs them, even blocking a TRAINED jedi from using his mind trick and reversing it back onto him. She had 0 training or help from anyone and pulls off these advanced Jedi moves out of thin air.
Remember in The Empire Strikes Back, Luke goes to find Yoda and how much Luke STRUGGLES just trying to learn to lift a small rock? Then how he lost the fight to Vader (costing him a hand in the process), he couldn't magically do EVERYTHING and wasn't good at everything right when he needed to.
Also she can fly, fly the falcon which she never flew before. How? It's never explained within the movie at all, she just "does it" out of thin air.
However in some book released outside the movie they tried to explain it by her flying "simulation" things on a headset or something, though like most people, you probably never read it and thus most people don't know that information, the movie shouldn't need a book to expand on an already weak character, that's what the film should do.
You do realise Kylo was not actually trained fully, he had strengths but in certain areas, and when she managed to match him in combat he had also been shot, which normally fully drops any other person we see in Star Wars films.
Rey also had a more aggressive background life to that of Luke Skywalker, and remember in the 1st film he started to learn quickly how to defend himself with blast shield covering his face so 'blinded' while blocking the attacks from the training balls (whatever they are called) which fires low powered shots at him.
Their shooting skills pretty much match and also their flying skills, while Ren did learn to perceive a person's mind quicker and with more detail (Luke could only generally I got a bad feeling) she could not force Kylo and only a weak minded trooper.
But then he was facing Darth Vader and not Kylo, and no comparison between the two tbh and would had been silly if he even survived like he did without even partial training from Yoda.
In the TFA did Rey ever lift anything with the force?
In all the narratives they have shown this to be one of the most difficult techniques to master (including in the animation series).
Anyway with partial true Jedi training Luke finally managed to defeat Darth Vader who was not just fully trained but also incredibly strong in all ways of the Jedi.
But both films (and especially Episode V) created some leeway for their narratives-plots-action with regards to Luke and Rey.