To be explicit: The person you're responding to didn't say it but they have as a premise that when it comes to political systems, lack of empathy is the defining characteristic of fascism (I'm not saying I agree with the premise, I'm saying they had this premise). If you accept this, then their argument is not logically wrong. In contrast, your example is logically wrong. In the "two feet" example you're point at one attribute of something, not a defining characteristic. The correct example would be "All bipeds have two feet (by definition). Bob has two feet, therefore Bob is a biped". The gibberish you produced is logically wrong, while that of the person you're talking to is not, but you're too stupid to understand that.
> Fascism is a lack of emotional intelligence, which is basic intelligence. Empathy and compassion are a form of basic intelligence. (_AND THEREFORE, fascism lacks empathy and compassion_)
This doesn't follow. Fascism can be a lack of emotional intelligence, emotional intelligence can be a form of basic intelligence, empathy and compassion can be a form of basic intelligence, and it can still be the case that you lack emotional intelligence but have empathy and compassion (you might simply lack in other aspects of emotional intelligence).
Here's a section just for you: "When disagreeing, please reply to the argument instead of calling names."