So your proposal was voted down because it would have had a negative impact on the other managers work/life balance. Sounds a valid reason to vote it down. You were in favour because it would improve your work life balance. This is always the problem for some the status quo is better for others something else might be better.
It's almost ironic; the reason that they don't have any friends outside of work is because they spend all of their time at work. As it is, when they cover weekends (currently, one in 4) they end up working 12 days straight without a day off. It became natural to want to hang out with the people you already spend 70% of your life with. Most of them even hook up with/date each other, which has negative consequences when those relationships end.