Handling "I’m busy right now"

"I am busy right now" is sometimes true and sometimes a polite exit, and the way to tell is to offer a specific alternative time. A real constraint produces a real answer. A polite exit produces vagueness. Either way you learn something, and offering the alternative costs one sentence.

The test is a specific time

Suggesting a concrete alternative separates the two cases almost every time. Somebody genuinely mid-task will often engage with the specifics. Somebody using it as an exit will stay vague, and the vagueness is your answer.

Do not argue with it

Even when you suspect it is an exit, treating it as one out loud is the wrong move. It insults the person and closes the street. Accept it at face value and let the alternative time do the work.

Write down what they said

If it produces a real time, that is a callback and it needs a date attached to it now, at the door. This is the most commonly lost kind of callback because it feels like a brush-off even when it was not.

Common questions

Is "I am busy" a real objection?
About half the time. Offering a specific alternative time is the cheapest way to find out which half you are in.
Should I ask what time is better?
Better to propose one. An open question invites a vague answer, which is the outcome you are trying to avoid.
How do I log it?
As a callback if they gave you a time, and as not interested if they did not. Logging every brush-off as a callback fills your list with nothing.