I periodically need to remind myself of this. Sometimes, the angst gets a bit thick in a confusing way and this is the problem, es explained by Oliver Burkeman:

[Other people’s emotions aren’t ultimately your problem. This phrase winds some people up, because they worry it means carte blanche to be a jerk to others – to treat them like dirt, then saunter away, complacently reassuring yourself that you needn’t take responsibility for the emotions you just triggered. But I don’t think that’s what it means. I think it means that at the end of the day, it’s a fool’s errand to make your sense of feeling OK dependent on knowing that everyone around you is feeling OK. Taken at face value, the information that someone is upset because you’re not doing what they wanted you to do is just that: a report on the state of their emotional weather. It doesn’t inherently implicate you at all. You might have good reason to do whatever you can to improve their weather in this case. But then again, you might not; it might be one of those cases where they’re just going to have to deal with it without you. As a factual matter, all callousness aside, the problem belongs to them. Allow other people to have their own problems!

And of course it turns out, time after time, that the people you thought would be furious with you… aren’t. You take some decision to use your time in a way that seems likely to invite anger or disappointment from someone else – yet the anger or disappointment never materialises. People find some other way to deal with the situation. Or they’re too wrapped up in their own troubles to be thinking of you at all. Whereupon you realise, with a start, that you were always somewhat freer than you believed to do what you wanted with your life. You only ever needed to face the consequences – and half the time, there weren’t even going to be any serious ones.

The above quote is from a mass-emailing – I don’t see a link to an article. Here’s Oliver Burkeman’s postings.