Can a police officer deny my request for a ride home being a "intoxicated" minor?

Yes, they can deny your request. Then when you get killed staggering in the street in the dark, your parents can sue the police and the city for gross negligence. They have a public duty to arrange for you to be transported to a "safe location", such as the local precinct, where you can be picked up by someone who can take responsibility for you, assuming there is such a person.