Ms. Liu, yesterday I joined a Chinese conversation group. I said "Hello" to a teacher, but a Japanese friend told me that was impolite. Is that true?

It's not really impolite. "Hello" is a very common greeting, and no teacher would think you're being rude because of it.

Then why did she say you shouldn't say "Hello" to a teacher? I felt so embarrassed at the time.

She probably thinks you should be a little more polite when speaking to a teacher. At school, students usually say "Hello, teacher." When meeting for the first time, you can also say "Hello, Teacher" in the more respectful form.

So it was just that my wording wasn't natural enough, not that I was disrespecting the teacher.

Exactly. And in a relaxed Chinese conversation group, if the teacher is about the same age as everyone else, simply saying "Hello" is perfectly fine too. It really depends on the situation.

Then next time I'll say "Hello, teacher" first, and after we get to know each other, I'll use a more casual greeting.

That's the safest approach. Don't worry too much because of one person's comment. It's not as serious as you think.