Do you think my best friend will get the point if I'm passive aggressive because he forgot my birthday
How did you feel when you found out that your bff forgot your b-day?
I'm extremely resentful about my best friend for this reason.
No one likes to feel dismissed on their b-day, however, reacting passive-aggressively to your friend over a forgetful mistake is too much. Forgive and forget this incident and use this to strengthen your relationship with your friend.
But I can't forgive him
If you can't find it within yourself to forgive him this friendship doesn't have much of a future. There will always be some tension between you from the grudge you're holding.