Donald Rumsfeldt had a way of speaking in public, where to make his point more forcibly he would pose questions and answer them. Has Saddam Hussain bombed his own people? Yes. Has he begun the manufacture of weapons of mass destruction? Yes Are we prepared to see him terrorise his neighbours? No (This is not necessarily an accurate quotation, but just an example of the sorts of things he said).
But what interests me is this form of rhetoric which involves posing loaded questions and providing answers that make your point. Another exponent of this was Josef Stalin. In his case it has been seen by some historians as a technique he learned during his childhood education in a religious seminary. It was a form of catechism.
So what is the rhetoric called? Is it catechismic? The word does not exist (at least not in the OED) as an adjective.
Edit. I have briefly looked at the former question.It is not entirely a parallel example – the OP complains that his wife does it in the course of everyday conversation. I am primarily interested in the development of an argument through this process. But the former question did bring out some interesting words – e.g. sermocinatio,- @Sven Yargs – which unfortunately does not have an OED entry. But I am also fascinated by the link to catechism, which I believe may be the provenance of this in some politicians. Someone has now come up with a suitable adjective – below.
Answer. I think the closest answer has been supplied by @Old English Lapdog. It seems to be the case that there are two distinct elements to this. One is that it follows the religious practice of teaching by question and supplied answer. In that sense it relates to catechism. But in building an argument it is rhetorical. The word catechetical in its OED (sense 3) includes a reference to Socrates. 1711 J. Addison Spectator No. 239. ΒΆ3 Socrates introduced a Catechetical Method of Arguing. He would ask his Adversary Question upon Question, till he had convinced him out of his own Mouth that his Opinions were wrong. So I am prepared to accept catechetical as the answer.
Best Answer
I believe that the closest one will come is, indeed, catachetical, or catechetic - the 3rd meaning given in the Oxford English Reference dictionary : "consisting of or proceeding by question and answer." Unfortunately, there is no mention of rhetoric here. Since there actually appears to BE no word describing exactly that which you seek, may I suggest a new word? Catachrhetoral?...(catachrhetoralism.)