I want to know the name of movie I saw a long time ago. I just remember in the beginning part, there was a boy who just moved to America (around the industrial era). The kids at school make fun of him because he can't pronounce the "th" sound and says "tick" instead of "thick." He also spends time in front of the mirror practicing. The other kids also give him a banana and he doesn't know how to eat it, so he eats it with the peel.
I think you're talking about the short film The Immigrant Experience: The Long Long Journey from 1972 about a Polish immigrant boy named Janek who has problems fitting in. An online article mentions that he's teased by his classmates (who call him a 'greenhorn') and eats an unpeeled banana. He finds work at a slaughterhouse at some point. Here's a clip.