Asklemmy

First, I'd say it depends on the rumour. But in general for a sufficiently serious rumour:

Being "wrong about me" wouldn't be the thing I'm pissed about. Anyone can assume the worst of anyone else, god knows I've done more than my fair share of that. But to spread a rumour goes above and beyond in level of malice. They showed that they, 1, didn't care whether what they were saying was the truth or not, 2, didn't care how it would affect me if they were wrong, and 3, are willing to ruin someone else's social standing to improve their own since that's usually why people spread rumors. Without further context to the contrary, these are systemic traits of a horrible person and strongly suggest they'll do it again no matter how sorry they say they are.

No. That's some schoolyard bullshit. Tolerate mistreatment, and you'll risk normalizing it.

No. They will go to the re-education camps with the rest of the traitors when I rule the planet as Grand Overlord.

Did they pass on incorrect information believing it was correct? or Did they spread a rumor because they didn't like you and they knew the info was incorrect?

Huge difference.

It's a one time thing. People can - just like children - come to the wrong conclusions. If they stay on your side after the first time, they have understood you, and are understanding you from their perspective.

But if they continue to gossip about the next thing about you, they just wanted to bury the shit from before.

Getting older I am able to see the cues of 'gossip' and I throw all that shit to the back, and use opportunities to address my friends or coworkers about it indirectly to get a proper perspective.

Spreading rumors about someone is a genuinely nasty thing to do to someone. But even the best of us can probably spread information that we think is true and important but is really a fabrication.

I guess to me the difference is: were they genuinely mistaken and are now aware of their error and how they can avoid similar errors in the future, or are they a gossipy bitch?

Whatever I feel like. I wouldn't decide on a whim but consider my feelings properly. Forgiveness is not a rational thing IMHO. Edit: typo

It depends on the situation - did the rumor cause serious damage to my close personal relationships, career, etc? Are they willing to take responsibility for lying? Did they spread a rumor because they themselves believed it was true or with the intention of causing me harm? Have they matured as a person and is the apology sincere? I’m a forgiving person so I would most likely accept the apology if it was genuine and not too harmful.

... No, they knew they were wrong about me because they would have had to make up the rumor in the first place. What a dumb excuse.

I wonder if it's usefull if people think you don't know that they know that you're a murderer. When in fact, you're not.

It happened to me at work and it was a very bad period. Even if it ended well for me, no forgiveness.

Forgive, yes, but I'm never trusting them again.

Nope. They would be DTM(dead to me.)