How do I convince my parents that it is OK to become a Catholic?

There are good reasons for not becoming a Catholic, but your parents have not presented any. The problem is that the Catholic overarching semi-Pelagianism parallels some Protestant Arminianism. My guess is that unless your parents are Calvinists, there isn't a huge amount of difference between the two faiths. Both sides love God and want to please him. Both sides reach out toward their neighbors in love. You have your two greatest commandments right there.