I would like to ask a question regarding something I am quite confused by. Why is it okay to wear leather from an animal slaughtered not in a kosher fashion yet you cannot eat that animal's meat? To simplify this question and keep it in context, let's keep this as our primary example. I think a cow would be the perfect jumpoff point for this question. If I understand correctly, the primary reason Jewish people cannot eat just any beef/meat from a cow is that it must be slaughtered in a humane way, according to certain laws, in order to spare the animal undue pain and suffering. Assuming this is the primary reason for this specific example, why is wearing the skin of this animal (cow) which may or may not have been slaughtered in a kosher way okay?
The short answer "Because G0d said so"
The longer explanation, fills up volumes of books explaining "why" Hashem said so. You can start with Maimonides "Moreh L'nivuchim' (Guide for the Perplexed), as well as all the books that comment on it. While one of the reasons for the laws may include the humane treatment, the laws of ritual slaughter are not just for humane reasons, or for health reasons, or for any other possible reason, but for raising the meat that we eat to the level of a sacrifice (again among others). The requirement to treat an animal humanely is a separate restriction and applies no matter if the animal is to be eaten or not. Thus the requirement not to cause "tza'ar baalei chaim" (pain to living creatures) would require one to kill an animal humanely, whether by kosher slaughter or some other means.
Note also that there are many means of slaughtering humanely (although shechitah seems to be the most humane) none of which will allow a Jew to eat the meat. Additionally, if a person treats an animal inhumanely, but does not cause it to develop signs of treifus (such as lung lesions), then the meat would still be kosher after shechitah. On the other hand, if he treats it completely humanely and just misses cutting both the windpipe and the esophagus (to the 51% mark) by just a fraction (such as 49.99999% rather than 50.0000001%) the animal is not kosher.
Given that the Torah does not forbid the use of an animal that has not been slaughtered by shechitah (it is mutar b'hana'ah) we see that if someone has violated the laws of "humane treatment", then he is the one who has done wrong. The sin does not attach to the object. Note that the Torah has to explicitly forbid the use of meat cooked in milk (for a non food purpose) (asur be-hana'ah) as well as forbidding the actual cooking itself.
Basically, the Bible says only eat it if it was killed properly. If it died any other way, you can feed it to your pet (i.e. you can derive benefit from it), just don't eat it. The same would apply to a cow that died of old age! There are only three categories of dead animals -- "kosher slaughtered"; "kosher slaughtered but it was going to die soon anyhow of disease or injury"; and "died some other way."
Presumably, eating something signifies a deeper connection.
Something which is surprisingly not mentioned by most of the commentators here is that the basic reason why do most of the complicated laws of kosher killing of animals exist is to get sure that the animal was really killed because of the human action, not died because of a unrelated disease. This follows from a general prohibition of eating meat of animals which died because of natural causes (see Shemoth 22:30, Dvarim 14:21).
The test example is the following. Assume you find a corpse of a cow in a forest. Will you be allowed to eat its meat? Surely you won't. Will you be allowed to use its leather for you clothes? Why, on Earth, not?!
The explanation that shchita minimises animal's suffering is probably very modern (and, honestly speaking, a bit controversial). If you are looking for a kind of "social" or "cultural" explanation for the status-quo halacha, I think this is indeed more related to the ancient fear of eating animals which died because of unknown and perhaps dangerous for human diseases.