Remember folks, gender is a grammatical construct.
And another thing. Why is it "spinster?"
Shouldn't it be "spinstress?"
A spinster should be the default form: a man.
A man who is unmarried past the realistic point of marriageability (with a desirable spouse of course). So depending on your definition of "realistic" or "desirable," a man's spinstership would begin at what, mid-seventies? Others say puberty. Totally depends.