Father's Day is normally a day that is set aside for the entire family to do something together. At least, that is what I did with my children. I have been a father for over 30 years, and I don't remember ever being angry on this day. Instead of being defensive, if I were you, I would consider heading back to my father and apologizing for what I said. See if I could do something with him. I myself, spent a lifetime at odds with my father, but no matter what, I always wished him Happy Father's Day on Father's Day, and would later tell him that we needed to get together and do something. You have to set this day aside, to forgive your father for whatever wrongs you think might have been committed by him to you, and make an effort...a hard effort to do something with him. Lay aside the videogames, working on the car, whatever. Father's Day is recognition of the person who has made a concerted effort to be there for you since the day you were born, that is what this day is all about. And yes, if in this screwed up culture, your father may be a stepfather, so what? That person should still be there for you, no matter what you may think that person's faults are. A parent is a parent, no matter how they got there. Acknowledge that fact with a little attention. Bill Cosby summed this day up a long time ago with a small little story:
"I wanted a son. You know, a son to carry on the family name. A son to be proud of...yes, that is my son. Yes, my son. My son the doctor. Is that your son? Is that YOUR son who just made the touchdown? Yes, that is my son. So...you take the time to throw the ball around with him. Show him the finer points of the game, make sure he knows the correct 3-point stance. And during the game, after he just made the touchdown, and the television crew comes up to him to congratulate him, and ask him how he got so good, he stands in front of the camera and says, "Hi Mom!"."
That is the bane of the father. So you see, we father's feel that when our children admire us, and tell us that we are okay, and that we count for something in their lives. We feel like we have counted for something for our children. That is what your father's "freakout" actions tell me.