You are confusing two similar looking verbs: पढ़ाना 'to teach' and the one we have used previously, पढ़ना 'to study, read'
Thanks for the clarification. It's easy to get confused with these two
I think you will have seen this in Russian, I think it's similar to Perfective and Imperfective verbs... (btw... have you finished those top seven trees? Very impressive!)
पढ़ाता(Padhaata) doesn't mean "reads". It specifically means "to teach". Padh is the root form which can mean reading as well as learning/studying. But Padhaana specifically means to teach.
If you want to say - "Peter reads to Raj", it could be translated as "Peter Raj ko padh kar sunaata hai".