Standing up for what's right even when it costs you

Got passed over for a promotion because I wouldn't throw a coworker under the bus to make myself look good. My boss basically said if I had just taken credit for his work we'd be having a different conversation. But I couldn't do it. My kids look up to me. How can I teach them about integrity if I don't live it? Some things are worth more than a paycheck. Wanted to rant about that somewhere it would make sense.