Here's what wrong with this syllogism.
1: Socrates is a man.
2. All men are mortal.
3. Therefore ...
What's wrong is the movement from 2 to 3. It is not a question of deducing that Socrates is, or is not, mortal. You don't care whether Socrates is mortal. It's a question of: woah! Wait up. All men are mortal? You shit me, perhaps? I'm going to die? The problem, in other words, is that the syllogism requires that you consider, carefully, each step; and if you do that, there's really no way to get past step 2.