Should I share my own experience when supporting someone?

Yes, later and briefly. Two signs it's time: they ask you directly, or the worst of it has passed and they've started wondering how other people got through. Even then, a sentence or two is usually enough to tell them they aren't the only one. Then hand the floor back with a question about them. A useful check is whether your story left them more room to talk, or less.

For the urge to share before then, Susan Silk and Barry Goldman's ring theory has a short rule: comfort in, dump out. Picture the person in crisis at the center of a set of rings. You offer comfort to anyone nearer the center than you, and you vent to people further out. If what you want to say is mostly about your own feelings, take it to someone in an outer ring.

Because it moves the spotlight. However kindly it's meant, the sentence claims an understanding the other person hasn't had a chance to confirm, and it usually comes right before your own story, which can leave them comforting you. The "exactly" is also hard to back up. The same diagnosis or the same layoff still happens to a different person, with different stakes and a different history.

Patricia Frazier's research on supporters points to where it can come from. Supporters who were more distressed themselves gave more unhelpful support, like minimizing the other person's problems, and that seemed to have more to do with their distress than with not knowing better. The phrase wasn't what they studied, but I suspect it's often a way of steadying yourself.

Then answer. A direct question is an invitation, which makes it a different thing from steering the conversation toward yourself. Answer what they actually asked, and keep it shorter than you want to. People in that spot are often after one piece: what happened next, how long the worst stretch lasted, what you wish you'd known sooner. Give them that, then check whether it helped or whether they want something else. Leave out how hard it was for you unless they ask for that part too.

Related: How to support someone in crisis