Like so many of the beliefs of Jehovah's Witnesses, their explanation of their beliefs held in regards to celebrating birthdays crumbles quickly.
1) They immediately admit there is no Biblical prohibition against it.
2) They then draw a conclusion based on the only two birthday party stories in the Bible where a person was essentially murdered.
3) They make the claim that celebrating a person's birthday is in fact theft of glory belonging to Jehovah.
So, it's just an opinion with little evidence to support it. Just like so many other non-biblical self adopted prohibitions.