I had the opposite experience with my dad when it came to playing golf. In sixth grade, I became the second serious golfer in my extended family. My aunt, an Air Force officer who won military tournaments on occasion, was the first.
Dad thought caddying was OK because of the money, but did not think much of golf as a sport. He begrudgingly let me play - I told him I had know the game to caddy - but he was never very supportive. Part of this ties to the fact that he was my Little League coach for five years. After the sixth-grade summer season (1962), I told him I didn't want to play baseball any more. I wasn't much good at baseball, and got limited playing time because my dad wanted to be fair to other players. I think me dropping baseball really soured him on golf.
He thought golf was a sissy sport, and said a person got more exercise doing 10 pushups than playing a round of golf. In part, I think he may have been like Francis Ouimet's father in the movie, "The Greatest Game Every Played." He was afraid the rich guys would never accept me as a golfer (although public golf courses were on the upswing at the time).
When I was in my early 20s, he went out and watched me play one time; he caddied for me for 15 holes, until he got tired and gave me the bag. I broke 90 quite readily from the back tees, and he admitted it was nice to walk around the course. I asked him along the way if he wanted to try some shots, but he kept declining.
So, it's nice to know of parents who support their kids playing golf. But, as iacas says, "keep it fun."