"Never too busy for you!" is a well-known love catchphrase. Let's assume Mary (Peter's girlfriend) asked if she might meet up with him for lunch. "I am never too busy for you, my dear," Peter could say. This implies that Peter can make time for Mary regardless of the circumstances, simply because she is one of his top priorities. "I'm busy" would also be useful if Peter isn't interested in Mary. As humans, we have a tendency to use the excuse "I'm busy" to avoid doing something.
The other possibility is that Peter is truly occupied. If he's concerned and wants to see Mary for lunch, he'll say something like this: "At that time, I'll be having lunch with one of our valued clients. Is it possible to accomplish it tomorrow?" He would essentially try to explain why he is busy rather than just saying "I'm busy."
Most of the time, the "I'm busy" response is a spontaneous one that individuals use as a filler when they don't want to express "I don't want to do it." If they really wanted to, they'd find a way to do it, perhaps not right there and then, but at a later date.
You've almost likely been offered the "I'm busy" response, or you've used it yourself to get out of a sticky position at work. Everyone is occupied out there, when they are not working, they're in a meeting, dealing with traffic, picking up kids from school, parenting, doing housework, and possibly going to school. The list goes on and on. So, by saying you're busy, you're implying that the other party isn’t or won’t have something else to do at the proposed time, implying that what they're talking about isn't a top concern.
Remember that being busy does not always imply being productive, so don't use the excuse of "I'm busy" as an easy way out when confronted with a situation that requires your attention. Instead, discuss what you're working on and how it's keeping you busy. This will come across as more professional, and the other person will accept it more readily.
Everyone is busy these days, and someone would like to hear about how you manage your priorities rather than how your priorities are managing you.
Now it's your turn,
Please feel free to express your thoughts in the comments section for further debate. We feel that the solution to every problem exists; it's just that we don't express ourselves sufficiently.