Are the logical divisions you make in your mind really indicative of anything other than your arbitrary personal preferences?
"It is possible for a man to provide care" is not the same statement as "it is possible for a sexually dimorphic species in a competitive, capitalistic society (...add more qualifications here) to develop a male-dominated caretaking role"
You're just asserting that you could imagine male nurses without creating a logical contradiction, unlike e.g. circles that have corners. That doesn't mean nursing could be a male-dominated industry under current constraints.