I read a very informational article on the differences between and the logic behind A4 and US Letter paper sizes. The A series of paper is based on the ratio of 1:sqrt(2), or 1:1.414, as a paper with dimensions of that ratio can be folded in half length-wise and the resulting size retains the ratio. The US series does not keep its ratio, but skips between sizes.
Which raises the question, why the difference at all? If both sizes are arbitrary, why bother with maintaining a difference. The answers are long and involved, and mostly outside the scope of this article. At the core, however, it comes down to one thing: A4 isn’t an arbitrary size.