Why is a "thing" called "东西" and not "南北"?
There were two large markets in ancient Chang'an (长安/長安) city of the Tang (唐) dynasty, one called east market (东市/東市) and the other one called west market (西市), gradually people perfer to say to buy east and west (去买东西/買東西) rather than to buy goods in east and west market (去东西市购买商品/去東西市購買商品). The new business district West Market of Great Tang (大唐西市) has reconstructed on the old site of the ancient west market in Xi'an Shaanxi (陝西西安/陕西西安) today.
The meaning things was developed through a series of semantic extensions.
「東西」originally literally meant east and west, then developed the meaning from east to west.
Later, it gained the meaning of the four cardinal directions (i.e.「東西南北」).
東西 (4): 猶四方。
唐 杜甫 《無家別》詩：＂我里百餘家， 世亂各東西。＂
宋 晁補之 《魚溝懷家》詩：＂生涯身事任東西， 藥笥書囊偶自齎。＂
Then it acquired the meaning of the products manufactured or natural resources acquired from all directions (東西南北).
東西 (6): 物產於四方，約言稱之為東西。古代亦以指產業。
- 宋 王溥 《唐會要・逃戶》：＂大中 二年制：＇所在逃戶，見在桑田屋宇等，多是暫時東西。＇＂
Finally, it became used for today's things in a very abstract manner, as in the following Yuan Dynasty quote:
東西 (8): 特指人或動物 (含愛、憎感情)。
- 元 馬致遠 《青衫淚》第三摺：＂但犯着吃黃虀者，不是好東西。＂
The usage and meaning extension is quite clearly traceable in historical works.
Basically, 東西 is short for 東南西北, and originally meant resources and products manufactured from all directions > things. It is not 南北 because 南北 is another word meaning northern and southern regions.
Likely from 动使, short for 动使之物, generically referring to "things", originating in 五代 to 两宋 period.
The theory that it came from 东西市 in Tang Dynasty (唐) is unsupported by evidence.
东西市 originates in Han Dynasty (汉), around one millenia earlier. But no such usage of 东西 is found in any material throughout this period. In fact, the earliest usage of 东西 as "things" dates to Song Dynasty (宋), long after Tang ended.
A short article for reference: http://www.guoxue.com/?p=3764