I had an issue with contractors not giving us the corrections we needed, resulting in back and forth for weeks. Finally, I insisted that we have a meeting to go over every detail that they had not done. The PM was on the phone and kept implying this meeting was a waste of time. Finally, I blew up and said, "Oh, are we boring you? Is our work too tedious for you? We could let you get onto more important things if you have more pressing issues at hand." Finally, she shut up and we got the report finished.

My boss reacted similarly to yours. I thought she would be upset with me but she said to me after the meeting, "I think we need to find a new firm when this contract is up." It's what finally got her to see the light.