In today's social media world, debate is often broken down to the sharing of a meme or a single tweet of information, often in the form of an anecdote meant to represent one side's argument. And while it is true that the plural of anecdote is not evidence, there is actually some validity to the use of a single example to represent a viewpoint - but it DOES matter what that viewpoint is. The nature of the argument itself is what determines the validity of anecdote. Not all examples are equal.
I will illustrate this with a specific specimen (thereby also demonstrating my point - a single illustrative example can act as the only evidence needed to proof a theory). In the discussion over problems with the criminal justice system, and in particular the treatment of black youths by law enforcement, both sides like to use a specific instance, perhaps even a person's name (Tamir Rice) to represent the idea that black people are not treated fairly. The response of those who call this an attack on all law enforcement often comes in the form of a related a specific instance where the police did their job correctly. On the surface it's a stalemate - each side has their anecdote and they feel totally vindicated in their correctness. The problem is that the arguments are not the same, so the evidence backs up one but not the other. Observe.
A current 'viral' facebook post talks about a police officer shot to death after trying to taze a suspect. Another one describes a black man who was pulled over for speeding where the officer treated him professionally, he responded with politeness and cooperation, and the officer let him off with a warning. In both cases the underlying argument is that the police did good. Therefore, if the police did good in one instance it proves that all police always do good. But that's not how logic works.
On the other side, they'll point out how a South Carolina police officer shot an unarmed black man in the back, all captured on video. Or simply mention Tamir Rice. At it's core, these anecdotes are saying that police did bad. In broader scope, they're saying some police officers sometimes do bad things. It's that difference between absolutes and exceptions that matters.
You can list a million examples of something happening (cops do good, gun owners are responsible, Republicans aren't racist) and it will never prove the universality of that fact. Because you simple need to post a single opposite occurrence (cops do bad, good guy with gun shoots innocent people, a majority of Republicans think Obama is Muslim) and you've proven that there is no such thing as 100% perfection.
And it's after we accept the fact that things aren't perfect we can start to discuss how to improve them. Not all cops are good, not all cops are bad, but if some cops are bad then we should accept that a single bad cop is a problem worth addressing when their mistakes can lead to the death of innocent people (and there is plenty of statistical evidence that the criminal justice system is biased against blacks, so we don't need to rely on anecdotes for that).
You can argue against the evidence, you're free to say that the percentage is so small it's not worth worrying about, you can say that one specific situation doesn't prove a widespread problem. But you can't use your anecdote to argue for universality. You can't dismiss the counter-argument with more of the same. There's a difference between saying all and some. To deny the some doesn't exist is delusional and it doesn't advance the discussion in any way. Logic exists, whether you want to face it or not, and you can't tweet your way around it.