I personally believe birthdays are not allowed because it's a cult and cults need members to avoid mixing with "worldly" people. This of course does not apply to anniversaries.
This. Birthdays are a threat to the invisible walls that are built up separating JWs from normal people in two ways that anniversary celebrations aren't. The first, and probably most important, is that children have birthdays - their growth depends in large part on turning JW children into adult members so it's important that they keep the children segregated from normal people in order to properly indoctrinate the phobias of the outside and prevent them from developing a support system outside the cult that they could potentially turn to when they have doubts. Second, birthdays are often recognized by normal people at work or in school, etc. Anniversaries are typically ignored unless you're close friends with someone. Again, it's about separating JWs from normal society.
That doesn't really answer the spirit of the question, though. But there are so many double standards - so many things are forbidden on the basis of pagan origins but neckties and wedding rings aren't a problem. Tattoos are bad but shaving is good. etc. etc. They'll always just ignore the contrast because when you look at it closely you realize that it's ridiculous. In most cases, too, it comes down to whether they can effectively use the rule to either reduce individuality (i.e. no tattoos and all men must shave) or reduce exposure to normal people (birthdays, holidays, etc). Forbidding an anniversary party doesn't really do either of those very well. Same goes for wedding rings. They're fine because not wearing a wedding ring isn't going to separate you from normal people and there's not much individuality expressed there in most cases.
There would also be some risk to them in forbidding anniversaries. Since many couples celebrate privately with a nice dinner or something this could generate a place where some "weak" JWs would rebel and perhaps realize that the cult was overly controlling. This is particularly a problem because this rebellion would be two people together, which could result in their discussing it and thinking about it together which would increase the odds that they discuss other issues that they have with the cult.