So, really, why test? What does it mean to say 'I passed my ___ kyu or my ___ dan test, when the person with whom you train might not be able to tell, or might not care? Why do *you* test? What does your rank mean to you? What do you think it means to other people?
Rank exists in martial arts for one reason, and one reason only: it is a very effective marketing and political tool (I'm not talking about teaching licenses; those have a few other purposes). Judo was the first art to use the numerical ranking system, and it was adapted from the Japanese board game go as a way of quantitatively measuring skill through competition. Other arts, including today many non-japanese arts, have subsequently discovered that numerical ranking and colored belts are very useful in creating, maintaining, and controlling a large membership base, so now most of them use some version of this system. (I've written about this previously at a bit more length in a few threads, including this one
Most martial arts organizations (especially the big ones) are basically multi-level marketing schemes, and like other such entities they must work hard to motivate people to want to move up the hierarchy. Thus, they will put a lot of emphasis on rank, and encourage their member dojos to do the same. You will find a lot of people in aikido who believe that rank is very important, and this is usually because they have been repeatedly told it is important by people that they respect. Also, our culture in the US usually lends a lot of weight to rank in martial arts, which is to the advantage of those who would claim or issue it. Finally, those who are insecure about their own skill level, whether or not they should be (and in aikido, many of them rightly are), will tend to cling to something like rank as a measure of their accomplishment in martial arts, since it is all they really have. Of course, when asked people will come up all sorts of other reasons why rank is important to them, but all of them tend to some variation on these few basic themes.
Incidentally, I happen to know your teacher and I don't get the impression he cares much about rank. Last time I saw him he went on at length about how meaningless rank is as a measure of actual ability. However, he still operates within a system where rank is very important, and that system really is larger and more powerful than he is, so for the most part he still has to play by its rules. Since you train in his dojo, you do too, but luckily for you your job is much easier than his.