Whether it is considered rude or not to not wish someone a happy birthday depends on the cultural norms and the specific relationship between the individuals involved. In many cultures, it is generally considered polite and thoughtful to acknowledge someone's birthday with a birthday greeting or well wishes. Forgetting or intentionally not wishing someone a happy birthday might be perceived as inconsiderate or indifferent.
However, there can be exceptions and various reasons why someone might not wish another person a happy birthday. For instance, they may not be aware of the person's birthday, they may have had a misunderstanding or disagreement, or they may not have regular contact with the individual.
If you find yourself in a situation where you haven't wished someone a happy birthday and you believe it might be appropriate to do so, you can still reach out with belated birthday wishes and a kind message. It's never too late to show that you care and that you remembered their special day.
Ultimately, communication and kindness are key in maintaining positive relationships, and it's essential to be considerate of each other's feelings and expectations, especially when it comes to special occasions like birthdays.