Older date

I had a date with an older man, 25 years old, and I am 19. I told my family about it and they didn't like the sound of the age difference and out right said that they do not approve. Still don't approve even though the date went well. 
Yes, I am 19, but I live in my own, pay my own bills, and I am very mature for my age. My friends range between 24-26, and I don't like the thought of dating another the same age as me because of the experiences I've had. 
Do I listen to my parents, or to my gut feeling??