Is it not simply a case of knowing you will want coffee/tea before the conversation/programming is complete, and not wanting to get disturbed in the middle of it? You sister, for instance, was likely to need to turn and thank your dad as the coffee arrived, neatly derailing any chain of thought. Similarly, since you wanted coffee, you didn't want to start looking at the problem until you have coffee in hand, so that you don't have to break to get it in the middle of trying to think about the problem.

Right now, I'm finishing up looking at my morning webpages before I go and get a cup of tea or coffee (I haven't decided yet) and actually start working.