As mentioned in the other answer, it is convention, but there is a bit of logic behind the convention. A time signature of 3/4 is taken to mean that there are three quarter notes in each measure, so the fact that there are six eighth notes in a measure of 3/4 follows from subdividing each of the three quarter notes into two eighth notes.
Logically, a time signature of 6/8 tells you nothing about how six eighth notes should be organized into groups of two and/or three, but if you assume that three groups of two is out because that organization is properly expressed as 3/4, the only other option is two groups of three. A time signature that would make this explicit isn't possible using the traditional two-figure system. Mathematically, you could say that it ought to be 2/(8/3), but that is rather complicated to figure out and somewhat counterintuitive (the modern approach to teaching time signatures overlooks their original function as fractions). In recent decades, you might see 2/(dotted quarter note), which is a bit more intuitive.
For compound meters with a larger number of beats per measure, another approach that has arisen in recent decades is to make the groupings explicit in the numerator, so for example 7/8 might be expressed as (3+2+2)/8 or (2+2+3)/8, but this can also be expressed with other notational conventions such as beaming, so the practice is far from universal. Besides, in some pieces with compound meter the grouping changes from one measure to the next. In any event, I've never seen 6/8 expressed as (3+3)/8.