Kis, I am a native English teacher. You are right when you say that "It's nice to meet you" is at the start and "It's nice meeting you" is at the end. I think what the teacher was trying to say is that "It's nice to meet you" sounds a bit formal and stiff in our language.
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kis7385It's nice to meet you ('s = was)Whatever you say, remember that it's never means it was.
It's nice meeting you ('s = was)