Of course, broadly defined, I did some teaching in the math center. Avoiding the word for describing the job was primarily to distinguish it from the teaching that involved designed lesson plans, official presentation, and grading assessments. Teaching isn't the wrong word, necessarily, but seems far less preferable to words that would maintain the distinction by letting the more formal activity be the one called teaching, and calling the help center job "tutoring" or "working in the math center."
Having done both, as an activity it didn't feel like teaching compared to the teaching jobs I held later on, so the distinction seems worth having (and certainly exists in the university culture in the USA, hence Steve's response). First, help from the center wasn't always explaining material. For example, I might quiz them for memorization, as any friend of theirs might have done, or more commonly I would mark up their proofs, projects, or problem sets (professors communicated to us if there was a major project we shouldn't do so), with no further explanation--a red mark on the line where something begins to go wrong being sufficient for them to figure out the material. Lots of students just wanted the reassurance they were on the right track or not. Second, when I did explain topics (the teaching part), it was never original presentation of material to the student, but revision for an exam or reexplaining to guide them through understanding a concept from their coursework they had difficulty with. It was never organized ahead of time, but a spontaneous response to whatever problem the student was having ("Show me the part of your notes you are having difficulty understanding..."), and thus was quite unstructured in form. It was never to more than two or three students at a time, and usually just one at a time. Basically, I served as a tutor provided by the university, and in fact organized less and presented less material than when I did work as a private tutor. It seems useful to distinguish between such an activity and the activity of presenting organized and original material to many more people for them to learn it and be assessed on it.
As an aside, the true "why" is that I had a financial aid grant that included working for the university, and sitting and reading in the math help center while occasionally helping someone coming in was a lot better slot than cafeteria work.
