"I do not celebrate the birthday!"
Translation:Eu nu sărbătoresc ziua mea de naștere!
There is nothing to indicate it is "my" birthday, thus, that should not a valid option.
It is not clear to an Englishman what this sentence means. It cannot be my birthday. Can it refer to birthday celebrations in general, or must we assume the everyone knows "the" particular birthday that is the subject of the conversation?