I'm going to break a friendship over a holiday disagreement
What was the holiday disagreement about?
Because he said he doesn't want any gift for his birthday
It seems the disagreement is very small. It would be best to avoid ending a friendship because of a small disagreement.
I was mad at him for having a different stance on present giving than me.
Friendships will come with disagreements, you can't always expect someone to think like you. Instead you should respect your friend's position on gift giving. Ending a friendship over something so small is something you may come to regret later.