The reality is, we're not family. I don't have to be sensitive to my family. If I don't like them, I can say and do as I please. If they don't like me, the same. I don't have to care about their feelings, I don't have to accept their life choices. I don't have to see them every day. I don't have to accomplish tasks with them. I can quarrel with them, and eventually they may choose to forgive me because of kinship, or not. Point being, there are precisely zero commonalities between family and work peers. And there shouldn't be.
The contrarian jerk in me really wanted to yell an epithet during training and say something along the lines of "What, if we're a family, I'm the racist uncle that your dad keeps inviting to dinner despite his offensive tirades and uncomfortable leering at your sister. Deal with it."
LOL. But in general I very much agree. Equating a workplace with a family is gross, and a bit cult-ish. I do think the workplace (and the world) would be a better place if we all tried to love each other like we do our own family, but there's a whole lot of other things family brings that would make the workplace a nightmare, the least of which is widespread manipulation, power struggles, mooching, and non-stop drama.
Don't those two usually come in pairs?
In the US this is like having relatives that worked with Al Capone
(Personally as an adult who continues to deal with difficulties regarding abusive family, I would feel highly uncomfortable with "we're a family" rhetoric- this is the exact rhetoric abusers use when abusing their family!)
You're right to feel uncomfortable; this is not coincidental.
You should view such comments with the same eye that you would view a someone that is always saying 'I love my wife/husband'. Companies either walk the walk or they talk and won't shut up.
You can leave a company, or the company can lay you off, or re-org and divest your department. After a year, you will not go to the company picnic. Just won't happen. Not a family.
Just as a small anecdote: this can happen. I do go to occasional picnics and parties my previous company chooses to make open to former employees. I'm already looking forward to an upcoming office-warming party, as I expect to see a bunch of old colleagues I really enjoyed working with.
There was not a single asshole during my time there. I resigned (over a year ago) to get some fresh challenges, so no bad blood either.