The Fool's Paradox With that interpretation, your argument can be translated as such:
A) Each fool a friend of someone S1
B) Each fool is a foe of someone S2
C) No foes of someone are also a friend to them
The conclusions:
D) No fools are a foe to anyone
E) No fools are a friend to anyone
I gather this is the intended interpretation of your argument. If not, explain how it isn't.
The conclusion doesn't follow from the premises; all that is necessary is that each friend S1 of each fool is not also a foe S2 to that fool. S1 =/= S2. Feel free to substitute cats and dogs into the argument form and derive nonsense.