Because there's bigotry in the statement itself. It's like saying "Shoot all gun owners" or "I hate the intolerant" or "Silence all censors." It's a statement that simultaneously says opposite things. It implicitly endorses that which it ostensibly opposes. It is literally doublethink. The person saying it is deeply confused.
If she were writing a mathematical proof then I would agree with you. From a logical standpoint stating "white male bigots should be fired" doesn't say anything about non-white non-male bigots.
However, in normal discourse context is not generally understood to be that of a logical proof. Things are implied and inferred by what's included or excluded from what's said.
So, for example suppose I were to say simply "white male high-performing employees should be promoted". Logically this doesn't contradict the statement "all high-performing employees should be promoted". But I didn't say that. I made a much more qualified statement regarding white males. Why did I qualify it so. It's natural to ask such a question. I would expect people to think I'm implying something about non-white non-males. Again - It's natural, and in fact part of normal discourse, to infer things from what people chose to include and omit from their statements (please let me know if you disagree with this).
Similarly, original statement was about white male bigots specifically, not just all bigots. It's natural, outside the context of a logical proof, to infer some meaning from that.
If I have on my shopping list "yams," do I fill the rest of the sheet with explicit exclusions like "not pudding?" No, they are all excluded by simply not having been included.
If we propose a raceless society, why are we mentioning a race? That's the weird part.
If I declare we need to eradicate all biting dogs in my town, does it make sense for me to also include biting rabbits on the list? To be arguing this deep into the problems of a unclear sentence is INSANE!
