I'm trying to think of the name of this fallacy, and it's driving me crazy. The typical situation is this: I make a claim, and list several examples supporting this claim. Someone then discredits one of the examples, focuses on that example, and insinuates that the entire argument is invalid based on this.
Example (I do not want this to turn into a political conversation, so please do not focus on the example topic in your response):
Hypothesis: Political campaigns have emboldened racists to be more open with their hate.
Evidence: multiple news articles showing examples of political activists acting in hateful ways this week.
Counterpoint: one of the articles was later shown to be a hoax.
Counter-conclusion: These articles can't be trusted, so your claim is false.
Your input would be greatly appreciated.