Look, I'd said, say you tell everyone when it is and nothing happens. It's kind of a slap in the face.
Or suppose they throw you a party, Chelsea had replied.
Then you don't know whether they're doing it sincerely, or if your earlier interaction just guilted them into observing an occasion they'd rather have ignored. But if you don't tell anyone, and nobody commemorates the event, there's no reason to feel badly because after all, nobody knew. And if someone does buy you a drink then you know it's sincere because nobody would go to all the trouble of finding out when your birthday is— and then celebrating it—if they didn't honestly like you.