At infants

I remember when I was in the infants (about 5 or 6 years old) the teacher asking me to work out something or other (can't remember what). I kept saying I can't. I can't do it! She said there's no such word as can't! So I replied I cannot do it. The look of exasperation on her face was a picture! But I didn't understand why at the time and for some time afterwards I never used the word "can't" but said cannot instead.