Respectfully, it seems that most people are trying to explain you precisely the part you don't have a problem understanding. And I see how you might feel this usage of question words can only have some truly esoteric grammatical reasoning behind it.
It's useful in any situation, when confronted with something mystifying, to ask yourself what might be missing from the picture. Imagine an alien biologist on Earth looking at a snake and wondering, "how can this worm have a spinal cord?" The answer being, a snake isn't really a worm and it didn't even always look like one.
There's a Czech proverb, Kdo chce kam, pomozme mu tam. Literally, "who wants where, let's help him there." (Meaning that the speaker washes their hands over someone they think is walking into trouble.) Now the same words in the same order wouldn't quite work in Russian, but this very saliently illustrates the logic behind this usage of Slavic question words: they're on one side of the scale, as it were, counterweighted by their definite counterparts in the second clause ("who"/"him", "where"/"there").
Thus кому как started out the same way, as the first part of a diptych; to use V.V.'s example,
Кому как, а мне русский язык нравится
— again, кому has a clear counterweight in мне, and, slightly less obviously, как corresponds to нравится. The rest is just the universal linguistic tendency to trim things. Кому как (and a few other question word duos, such as кому что or кто куда, as in that Czech proverb) saw enough usage in Russian to no longer need an explicit antithesis. (Not to mention that at some earlier point, they had stopped needing an explicit verb.) And so you can think of кому как as a snake: to find its evolutionary origin, you first have to find its lost limbs.