Edited: Glad I got to the hurried mess this was, before anybody saw it…
Teaching prepositions feels banging your head against the wall?
I don’t think so.
Linking two nouns with a linking verb + like is not the same as modifying a subject + linking verb with an adjective form functioning as an adverb.
She felt good.
Did she feel good?
Yes.
“How” did she feel?
Good.
Teaching prepositions feels like banging your head against the wall.
Does teaching prepositions feel like banging your head against the wall?
Yes.
“What” does teaching prepositions feel “like”?
Like banging your head against the wall.
“How” does teaching preopsitions feel?
“Like” banging your head against the wall.
“Teaching prepositions feels like banging your head against a wall” could be the answer to a “how” or a “what” question but it should still be considered a N=N structure. That can be demonstrated by reversing the order. “Banging yourself on the head feels like teaching prepositions.”
Either that or Fox had it here…
I think this is odd though because when a person says “He feels/ looks/ sounds like a teacher” they usually mean “He feels/ looks/ sounds like he “is” a teacher.” He “seems like” a teacher. Maybe he “is” a teacher, though not well respected. It is derived from the N=N pattern. It “is” the N=N pattern. Otherwise why would they they call it a linking verb? The “linking” in “linking verb” has to mean something.
In any event I think we can agree that there exists a useful distinction between “feels” and “feels like”.