Well for starters, I don't see any reason why anyone should believe that reading is the only thing that can bring you success, I mean there are people who don't read much(musicians) and they end up doing just fine.
I agree that the pursuit not knowledge will ultimately result in success, but it's how you utilize the knowledge that you've gained that matters. I mean reading is a good thing, anyone that says other wise doesn't know what he/she is saying.
If you feel that your parents are on your neck for not reading too much then that's ok because parents always want the best for us. If you're ok with the amount of reading you do then let your parents know that you aren't them and you have a right to read whatever you want and for how long you want.
Focus on the things that make you happy, focus on your passions and find a way to make it profitable. That is the only sure fire way to becoming successful that I know.
I hope this helps.