Why shouldn't people touch wild animals?

Some wild animals can injure or even kill us if we touch them and they react. Additionally, wild animals might carry parasites or diseases that we can contract from them. Another reason we shouldn't be putting our paws on wild animals is that we might set in motion some kind of interaction between these critters and people. If you set and example by touching animals in the wild, they might get the idea that people are "okay" to be near. Then these animals will approach others, some of whom might not react well, and then injury to a person and/or an animal can result. The best advice is probably to give the wild animals an appropriate amount of space and avoid any interaction with them.
It should also be noted that some species, when touched by humans, then carry a human scent and are therefore excluded from their group/ herd/ etc.