Do you get annoyed when people brag about how busy they are? As if being "busy" is a fucking virtue. Y'know what I mean? They say they can't attend to you because they have really important things to do. Or, more important things than to attend to you. And if so, it is also a word used to demean the respondant.
If you don't have time, tell me you don't have time. Don't tell me you were double booked, or was really busy, or was stressed from all that work. EVERYONE is busy. It's all relative. The word "busy" is such a subjective word that it can be thrown around with no merit. You will also get no sympathy like "Oh... I'm sorry to hear you were busy" because frankly, no one gives a fuck.
I could be busy closing three measly contracts. The president can be stopping three terrorist plots and consider that busy. But yet we treat our own business like it can really save lives. Just tell me if you're available or not. And if something can't be done on time, don't apologize or tell me you were busy, because that does not help the task at hand.