Why not a nice round decimal number, since we're measuring in the metric system to start with? Why not 100 mm, a "decimeter" in that system? In the original manufacturing formats, a decimeter would have held about an hour's worth of music, which is itself a pretty standard unit of time. The 120 mm version holds about 74 minutes by comparison, surely an odd measure.
Way back in the late 1970s when the format was being developed, two companies were working together to create it, Sony and Philips. As they were doing so, they were setting many of the standards that are common to us today, like the sampling rates and disc construction. Both Sony and Philips aimed at a 60-minute playing time, Sony with a 100 mm disc and Philips with a 115 mm disc. Various tales suggest why the 120 mm format was used, ranging from the story that the Sony president's wife liked a particular performance of Beethoven's Ninth Symphony that was 74 minutes long and wanted it to fit on one disc to the fact that Philips, through its PolyGram record company division, was well ahead of Sony in the manufacturing end and that Sony had to push for a different-sized format in order to make sure it didn't start out the CD business well behind its competitor.
Whatever the whole story is, you might stop and think that about how many things, from shelves in desks to CD cases to album art to DVD boxes to the size and construction of computers has been influenced by that decision, and that decision wasn't made with a thought towards any of those things. I try to remind myself of stuff like this when I get to thinking I can predict what's going to happen in the future.