I’ve heard of cases where not sharing vulnerability in such a setting led to others (who did) being offended and subsequent othering. While arguing the manager needs to be fired is a bit too far, you do need to consider the power differential and how it forces conformance from everyone.
Yes, if someone shares they were abused as a child, it becomes much more fraught to tell everyone you messed up two poached eggs while making brunch last weekend and you are not quite the chef you hope to be.
That’s why you have to volunteer to go first, because then you have plausible deniability about the expected level of vulnerability.