Birthday is a noun and an event. Annual is an adjective and a descriptive word. They are not the same thing and your comparison is meaningless. You are grammatically incorrect in this case.

First off, journalistic guidelines and grammatical guidelines are two different things. Grammatically there is nothing wrong with saying "first annual event". People seem to confuse the adjective annual with the noun anniversary. Annual simply describes the rate at which something occurs. It does not require a starting or stopping point. It's a descriptive word like smelly, loud, or repetitive. Anniversary on the other hand DOES require a first instance in order for it to exist. Let's say you are planning a fun event. Does the event have to take place -first- in order for you to describe your planned event as fun? NO. The same holds true for annual. If you plan for your event to be annual, you are free to describe it as such, and if this is the first instance of this annual event, it makes perfect sense to call it First "Annual Event", just like you'd be free to describe your fun event as First "Fun Event".

I think the drama has come from the area of journalism where they refuse to acknowledge the -plans- of people, organizations, etc. on the grounds that they report what HAS happened, not what is hoped will happen in the future. While "first annual " is grammatically fine, from a journalistic standpoint it is not because in those two words you are making -assumptions- about what will happen. Assumptions don't fly in journalism, which is probably why First Annual has received such a bad rap. People, businesses, organizations, etc are all free to make assumptions (which "first annual so and so" is doing in a grammatically correct way) but journalists are not. Somehow these journalistic guidelines evolved into grammatically "fact".