すべて, just like 'all', means 100%, or conversely 'none'.
The issues before you are between logical construction in Japanese and non-logical (implied context) construction in the English phrase.
The English phrase 'I don't choose all my courses' could just as well logically mean that you choose none of your courses (Don't choose any), but normally there is an underlying omitted context. Namely, 'but I do choose some/most of them.'
If you want to make the English sentence logically correspond to the implied meaning, you would need to say something like 'I am not allowed to choose every single course', or 'It's not like I can choose all of my courses'.
In Japanese, the underlying omitted context is not there. You are literally saying 'I choose none (not a one) of my classes'. This is why your friend suggested that you add a modifier.
「すべての授業を選びません。」= （授業の100％） 選ばない。[(100% of classes) I do not choose.]
「すべての授業を選ぶわけではありません。」= （授業の100％）≠ 選ぶ [(100% of classes) ≠ I choose.]