But it's a light icebreaker, no one wants a 15 minute sob story about how you were so depressed that year that you tried to kill yourself twice. It's not "say the first thing that comes to mind', they were asked to give a quick example, in a work environment, to co-workers. You're allowed (and expected) to self-edit a bit. As 'dark' as you really want to go there is that maybe you were having a bad year, and then X happend that was nice to turn it around. You don't talk about the time you took all those pills or climbed up on the roof.
As someone mentioned, it seems that if you don't have a good story, a lot of people decide to go straight to the pity party routine and see if they can out-suffer you instead.
How about a little awareness of the situation? Maybe next time, just talk about your trip to the grand canyon, and skip the part about going there because you thought you were dying of cancer (and the 20 minute follow-on about all the chemo)?