"Why are you asking?" versus "Why do you ask?"

Why are you asking Tom? He does not know the answer. Ask me instead!

versus

No, I have not seen Tom for quite some time. Why do you ask?

Is it correct? And if it is, why the difference? Is it not in both cases a single action ('ask') happening at or around the time of speaking?

I guess that the answer is to do with the fact that, in the first sentence, the pupil knows why the teacher is asking Tom, (in order to get an answer, which goes without saying), whereas in the second sentence, I do not know the reason the person who asked me whether I had seen Tom lately did so.

The difference here would be parallel to the difference between Present Perfect Simple –'I have repaired the car.' – where the emphasis is on the result of the action, and Present Perfect Continuous – 'There is grease on my hands because I have been repairing the car.' – where the emphasis is on the action itself, is more descriptive, and we do not know whether the result, getting the car repaired, has been achieved or not.

I disagree somewhat with Barrie.

For most verbs the simple present can be used only in a habitual sense:

Why do you hit him?*

is unambiguously asking about your habit, not about this particular instance. Why are you hitting him? or Why did you hit him? would be usual for that case.

For some verbs, particularly denoting mental state, the continuous is not normally used (or has a particular connotation if it is used), and the present is normal:

Why do you want that?

Why do you think that?

What do you see?

The verb ask appears to refer to an act, rather than a mental state; but it nevertheless can behave like those verbs and take the simple present.

*In ordinary speech, you may hear why d'ya hit him?, but this generally represents why did you hit him? not why do you hit him?

One of the uses of the present progressive construction is to describe something that is temporary. The event described in ‘Why are you asking Tom?’ is by its nature unlikely to last for long.

One of the uses of the present tense is to describe a present event, or, as in ‘Why do you ask?’ one that has very recently occurred. The present progressive can also be used in such situations, but with a slightly different emphasis. ‘Why are you asking?’ contains a hint that the speaker is suspicious of the motives of the other in asking the question.