Anthropologically speaking, you’re right. The term “shaman” has been applied by anthropologists to spiritual leaders and healers in many different cultures, primarily indigenous ones. However, the term was shoehorned by western anthropologist away from the Siberian indigenous people. It was theirs first, and in fact, more and more people who could be described, anthropologically, as shamans, are asserting their right to be called by the appropriate terms in their cultural language.
Leaving the anthropological world, and stepping into the neo-pagan and new age one, the term shaman has often been removed from anything resembling it’s original context, or even its academic anthropological context. As such, we find it prudent to not encourage the usage of the word to describe various neo-pagan or new age practices.
I recommend a quick look at the Wikipedia page on Shamanism for a brief rundown on the history of the word.
And as for why many consider it wrong to use the word to describe a New Age or Neo Pagan practice (These links apply to North American indigenous peoples because that is what I have the most knowledge of):
White Shamans and Plastic Medicine Men (Youtube)
There are no valid reasons whatsoever for thinking that we are more important than others. For Buddhas, who have unmistaken minds and see things exactly as they are, all beings are equally important.