My teacher said, "nowadays we don't use 'shall' instead of 'will'", but I read and hear that! Can you tell me about this contradiction? Thank you
Some people do, some don't.
In my (English English) dialect, I don't usually use either in affirmative statements ("I'll go"), but I use "will" or "shall" in negative ones ("I won't/shan't go"); but I always use "shall" in a question when I am asking for permission or confirmation: "Shall I go?" "Shall I open the window?"
But many speakers of Scottish English do not use "shall" even in questions, and say "Will I go?", which sounds odd to me.
My impression is that American English uses "shall" less than English English, but I'm not sure.
[Note: I'm using "English English" rather than "British English", because in the respect the Scottish English is different].