If you're hitting the wrong key, you're not actually reading it correctly. When I watch staiain play, I can 'read' the patterns he's playing. That is, I can understand what the patterns are when I watch him play, but if you asked me to play with that scroll speed, I would not be able to react fast enough to play even easy maps because I can't actually read the patterns.
When you press the wrong key, this happens when your brain cannot read the notes fast enough to actually figure out the correct finger to press. Instead, your brain just picks a finger and hopes it gets it right.
Of course, your brain can still make these mistakes once in a while even when you're perfectly capable of reading a pattern, but these usually result in a single missed note or 2 through an entire song.
Reading is something that you develop over time. As far as I can tell, the best way to train your ability to read is to avoid playing the same songs over again as much as possible. Learning to sightread beatmaps (in other words, learning to play completely new maps you've never seen before) will help develop reading skill faster than if you played the same few maps over and over.
3 months is still quite new to the game, so don't worry too much about it, you will keep getting better for a while no matter what you do.