We didn't believe that birthdays were wrong because some people got beheaded; not really. We believed it because we had unquestionably accepted an organization as being God's sole representative on earth, and that organization told us it was so.
That's exactly the right answer.
It's a little hard to pitch to coworkers, et al, though. After all, that CLEARLY makes them a cult, and to most the world, JW's are just those 'harmless but irritating people who wake me up every Saturday'.
Plus, you just KNOW that if you told someone the reason you didn't celebrate birthdays was because someone claimed god told them it was wrong....well....they'd look at you kinda funny and worry about your mental health. "I got better" doesn't work very well if they don't understand the context.