Hopefully they will understand that this is about what you want and feel is the best for you not what they want. Our son decided to decline his appointment to USNA and take his 4 yr NROTC scholarship to an out of state public institution. Sure, we were a little disappointed (his dad being an grad of USNA and mom spending 2 years there and knowing that it is a great institution) but we also knew that you really had to want to be there to successfully make it through 4 years. We told our son that this was a time to be selfish and listen only to his heart and not to make his decison based on what he thought parents, family,girlfriends, etc wanted him to choose. You get the same commission coming out of NROTC at graduation as your counterparts at USNA. There are definitely pros and cons to both and you need to make the best decision for yourself.
Talk to your parents and know that most parents want what is best for their child!