FOAB doesn't necessarily mean that the speaker is busy, there are several situations in which it can be used.
Scenario 1 - Using it to respond to a stupid suggestion with
indignityPerson 1: Hey you wanna go to the pictures?
Person 2: FOAB
Scenario 2 - Using it to dismiss somebody with
discontentPerson 1: Hey guys, what you up to?
Group: FOAB
Scenario 3 - Reflecting your