The most natural explanation is that the human gestation period is nine moon cycles long. The average gestational period is 41 weeks, and as it takes the moon 29.53 days to go through all its cycles, this is about 9 moon cycles and 3 weeks. Considering one would naturally count from the last missed period, this is a fairly acceptable answer.
The second is that Agrippa says that the magic square of luna is 9x9. It is impossible to make a magic square of 1x1 or 2x2 (well really only 2x2), so we have to start at 3x3. Going down the traditional planetary list makes sense and that puts luna at 9x9. This is not a very satisfactory answer.
The most common instinct is to say that nine is associated with Luna as the sphere of luna is associated with yesod, the ninth emanation. I have found no evidence to support this other than Agrippa's "The Scale of the Number ten" where in the column of "Ten spheres of the world." the moon is the ninth. The sepher yetzirah doesn't support this, assigning the moon to the letter tav. In fact in the only version of the sepher yetzirah that attributes planets to the sephirot, luna is on malkuth!
Crowley and others are little help, basically having accepted this as a fact with apparently no reasoning, as is quite usual of the GD teachings.