There is a solid discussion of this question (why does "how come" mean "why") on Word Detective.
First, the article says that your hunch that "how come" is short for something else is correct:
The final piece of the puzzle of “how come” is the fact that it is actually an abbreviation of a longer phrase, which, although not known with certainty, was probably “how comes it” or “how does it come,” meaning “how did this (event, condition, etc.) happen to be this way.”
Second, the brief history of the origin of "how come" is that:
It seems to have been an American invention of the 19th century, although similar forms date back several hundred years in English. The first appearance of “how come” in print dates to 1848, but since that was in Bartlett’s Dictionary of Americanisms and the phrase was described as being common at that time, it is almost certainly older. That was, after all, an age when slang and colloquial phrases were usually avoided, not memorialized, in print.