Parents object to marrying cousin

I am a guy who’s 20+, with a decent job and income in the city. I am going out with my cousin, C, whom I met at a family function about three years back. We had not seen each other for a long time, and spoke briefly and exchanged numbers before we parted.

Subsequently, we kept in touch regularly by phone and the relationship blossomed. We became good friends and shared many things with each other.