First of all, although the term 不能性 is comprehensible to me, and I believe to all native speakers, it is not an established term, and is not found in the dictionary. One would still understand this term though, as "Impossibility" or "Inability", made up of 不能 + 性 .
Back to your sentence, you are right about this sentence not making sense, as obviously we cannot
draw out the student's incompetence with all sorts of lecture contents. As aguijonazo has suggested in a comment, there is strong possibility that this is a type for 可能性, a common word meaning "possibility" or "potential".
Draw out the potentials of students with various lecture contents.
As a side note, the proper antonym for
不可能性, rather than
不能性. The latter is still understandable, but not established/standard. Just like the proper noun form of
impossibility, yet if I say
impossible-ness you'd still understand me.