The point is that they teach you that 'i' enters insert mode and '<esc>' exits it. This is not true! It it was true and 'i' and '<esc>' only switched mode, then

The point is that they teach you that 'i' enters insert mode and '<esc>' exits it. This is not true! It it was true and 'i' and '<esc>' only switched mode, then the sequence 'i<esc>' would have no effect. Instead 'i<esc>' leaves the cursor on another character.