I was a few years out of college and attending a budget planning meeting with my boss. It seems I was the only one in our department who could manipulate formulas in Excel (correction - I was the only one dumb enough to admit that I knew what a spreadsheet was) so as punishment....oops....I mean reward, I got to help my boss put together the budget numbers for our department.
At the budget planning meeting every manager presented their desired budget for the following fiscal year. The executives would question each manager on particulars of their department's budget and then make suggested changes - usually cuts.
The fun began when one manager did not agree with the cuts the executives wanted to make to her budget. She explained how her department would be unable to complete many projects if the requested cuts were enacted. The executives pressed on and said the cuts had to be made. She again went through the projects that were scheduled for the following year and showed that many would have to be postponed. Again, the executives said that project deadlines would be taken under consideration but the cuts had to be made. This manager was unrelenting. She continued to insist that requested cuts to her department would cause the whole company to collapse "Enron" style. It started getting tense. One executive wasn't sure what to do with the manager since she would not budge. Literally - she would not move from the podium. I think the executive contemplated calling security to have her escorted away from the podium. Another executive had to plead with her to take a seat so they could move on to other presentations.
My manager had not presented our budget yet. After witnessing the previous episode I immediately wanted to be anywhere but in that room. I was extremely nervous. My manager presented our budget, contested the suggested cuts every so slightly, and then sat down. I was relieved when it was all over.
On the way back to our office from the meeting my boss explained the rule. The rule is such: You are allowed to tell your boss "No" twice when you are instructed to do something you do not agree with. The stubborn manager in the above story should have accepted the cuts after having already contested the cuts twice.
This raises the question: What do you do if you still don't agree? There could be several reasons why your boss does not agree with you. You may be explaining your points poorly. Your boss may have other reasons that he/she has not shared (or cannot share) with you for denying your request. Your boss may be exposed to other business aspects that you are now aware of. If your boss is unable to explain to you clearly why your request is being denied then it may be time to update your resume.