At its simplest, in the West we have a thing for threes. Three bits of God, three little pigs, three branches of government (in the USA at least), "things come in threes", three books/movies in a series (a trilogy), stories that have a "beginning/middle/end".
Bottom line, the West tends toward organizing and thinking of things in threes. Some might even be superstitious about threes (perhaps a Pythagorean influence).
In China the number 4 plays a similar role. I don't know much about 'numerology' in China, save to say that recently the number 4 (which apparently sounds like 'death' in Chinese) has been considered bad luck. Here's a better explanation than I could give: https://www.quora.com/In-Chinese-culture-why-is-the-number-4...
To add a complication, Chinese tends to use the US convention (with the ground floor being floor 1), while the English convention is the British one (with the ground floor being floor 0).
By happy coincidence, then, the 13th floor is also 十四樓, ie the 14th floor, so you only need to skip one floor, rather than two. That explains why HK skyscrapers are so high.