All three of these arguments are valid (i.e. if the premise is true, then the conclusion must be true on pain of contradiction).

Socrates is a man.

Therefore,

Socrates is a man or Socrates is immortal.

Socrates is a man.

Therefore,

If Socrates is immortal, then Socrates is a man.

Socrates is mortal.

Therefore,

If Socrates is immortal, then Socrates is mortal.

One of these arguments is actually an identity (i.e. A, therefore, A). Which one?

So if all men are mortal, and Socrates is a man, then each of the conclusions above must be true, but they all seem intuitively wrong.