It's human nature. We do this in our personal lives and in professional settings as well. When we dig in our heels and refuse to change, very often the people who are most impacted have nothing to do with the original issue.
We're doing this on a national scale with the partial shutdown of the US government, now in its second week.
Both sides have entrenched positions. No one wants to be the first to blink. Meanwhile nearly 800,000 federal workers are impacted. Many have been furloughed; others (such as law enforcement, air traffic controllers, and the TSA) are working without pay. All of them have bills to pay and financial commitments they can't meet without the paychecks they rightfully earned and expected to get.
Each side believes they are right, but the result is something that's very wrong. Until both groups agree to let something go, this impasse will continue. Negotiators will tell you the best way to solve a stalemate is to find a way for each side to have some kind of win. I-win-you-lose may work in the short-term, but only builds ongoing resentment and the desire for retribution in the future.
How often do we have a "shutdown" of sorts in our business or personal lives? How can we work to create more win-win situations? Where should we be letting go for the better of all involved?