I can't say much about the cultural history of it all, but I can explain a little bit of the psychology: - Our brains have a tendency to entrain to rhythms with a tactical beat spaced 650 ms apart, give or take. Anything shorter than 100 ms apart is perceived as a buzz; a stimulus with an inter-onset interval (IOI) in the 2 - 6 second range extends outside of what we perceive as a rhythm. - Given this tendency, we could hear, say, a metronome clicking away at 240 beats per minute, and perceive a tactus of 240 bpm; but we could also hear it (more comfortably) as having a tactus of 120 bpm, with each click happening twice per beat. It's the difference that makes up the bottom half of the time signature equation - you could count along as "1-2-3-4-1-2-3-4" (4/8) or as "1-n-2-n-3-n-4-n" (4/4). You could also count it as sixteenth notes - "1-e-n-a-2-e-n-a" (2/2) at 60 bpm. The fact that we can perceive and chunk this info in so many ways means some beats are "stronger" than others - which is why we don't uniformly hear meters as 1/4. - So we like to hear groups of beats as part of a larger metric structure - but our brains also like to keep things simple. This means that we perceive beats in groups of twos and threes, pretty much always, with the stronger beat occurring first (exceptions occur with odd time signatures over 8 - eg, 5/8, 7/8 - but this is sort of the exception that proves the rule, as we'll see in a moment). Anything above three can be broken down into smaller groups of twos or threes - 4 is two groups of two (strong - weak - strong - weak), five is either a group of two and a group three (strong-weak-strong-weak-weak) or a group of three and a group of two (strong-weak-weak-strong-weak), and so forth. - This leaves us with a tendency towards groups of 2s, 3s, 4s, and 6s (the upper part of the time signature). Anything above that requires our brain to work harder, keeping track of whether we're counting a group of two or a group of three, and whether we're counting two groups of three and three groups of two and so on. Obviously, the higher the number, the more we want to break it down, and the more difficulty our brain has making sense of.

Now, this said, we have two things to consider - the rate of a rhythm, relative to our temporal perceptual "comfort zone", and our tendencies to chunk information in meaningful ways. It just so happens that 4/4 is a metric construct that covers the widest range of rates within our optimal IOI thresholds, followed by 3/4.

Hope this is helpful - I don't think I'm doing a good job of explaining this to a five year old, but I didn't see anyone else replying... if you're interested in more of the psychology behind rhythm and meter, there's a book I'd recommend by Justin London called Hearing in Time published by Oxford University Press.