POD to lilfox. 100%.
I am also going to say something that may be politically incorrect, but it is based on my own observations in the work world. If you are sensitive about gender politics, please mentally add the phrase "in my experience" to everything I say below, and don't accuse me of making offensive generalizations. This is what I have seen.
The "rudeness level" of your comments depends on whether you were talking to a man or a woman. A lot of women would probably be unduly shocked by what you said, and it would be overkill. Women also tend to over-explain, over-apologize, and seek permission to voice their needs and requirements in the workplace, and put pressure on other women to behave the same way. Women tend to use words like "I'm afraid" and "I'm sorry" when they are not necessary, and to behave like subordinates toward their peers.
Men tend to push for what they want and ignore subtle or deflective hints. You have to whack them over the head with a rolled-up newspaper to get their attention to the big picture. When women talk like men at work (and I don't mean crude language, I mean direct and without circumlocution), they get accused of being rude, Female Dog, etc.
Unless you were using a "hey, stupid", type tone what you said was not rude. You were also not apologetic, deferential and submissive. There is no reason you should be, unless that is necessary to your role in the heirarchy or helps you function in your workplace.