We’re all just so “busy” these days. “Slammed” in fact. “Buried.” Desperately “trying to keep our heads above water.” "Overloaded".
Busy is a catch-all term. When we say "busy," we're really trying to say something else — although what exactly that might be depends on the harried soul that's complaining:
I'm busy = I'm important.
Being busy gives people a sense they're needed and important. It's also a sign that you are self-imposing these measures of self-worth by looking at quantity instead of quality of activity. Busyness does not equal productivity.
I'm busy = I'm giving you an excuse.
Saying that you're busy is a handy way to outsource your responsibility to your irresponsibility. Since you're always distracted, you don't have to do anything for anybody.
I'm busy = I'm winning.
To say that “I’m busier than you are” means I’m more important, or that my time is more valuable, or that I am “winning” at some never ending rat race. What you’re trying to say with these responses is: "I’m busier, more in-demand, more successful".