The phrase it takes two to tango means that both people share some blame for an argument or other difficult situation. That fight wasn't just your coworker's fault: it takes two to tango.
After an altercation between siblings, one of them might say, "She started it!" That would be the perfect opportunity for their parents to note, "It takes two to tango." It essentially means that one person can't be solely responsible, since it takes two people to have an argument. This phrase was popularized by a 1952 song of the same name, influenced by the tango, a dance that requires a remarkable amount of coordination between partners. So it's not just about arguments and fights — it takes two to tango in plenty of other situations.