OK, this is becoming a somewhat pointless discussion because one or two folk here are reading into others' statements that which they wish to read to support their own arguments rather than the writer's intent.
And that is particularly the case with Sir Nicholas Houghton's answer to a question that was a part of, not only of a much longer and wider-ranging interview, but also just one of very many interviews between Andrew Marr and many politicians, commentators and military people. CDS himself has featured many times in these interviews and has commentated openly and far more politically on numerous subjects without any of those currently riding the outrage bus ever remarking about it. That has only really happened after one somewhat extreme politician has made a fuss about it. Where were you all when CDS and others were commenting on important matters with a link to politics before Corbyn got all up himself about it?
By the way, the transcripts of all the very many similar interviews are available. If you can't be bothered to find them I can provide links.
Given the number of misquotes and adventurous interpretations of Sir Nick's response, here are the actual words:
ANDREW MARR: Of course we now have the leader of the opposition who says quite openly he would never press the nuclear button. Does that worry you?
GENERAL SIR NICHOLAS HOUGHTON: Well it ... it would worry me if that, er, thought was translated into power as it were because ...
ANDREW MARR: So if he wins, he’s a problem?
GENERAL SIR NICHOLAS HOUGHTON: Well there’s a couple of hurdles to cross before we get to that.
ANDREW MARR: Of course.
GENERAL SIR NICHOLAS HOUGHTON: But the reason I say this – and it’s not based on a personal thing at all, it’s purely based on the credibility of deterrence. The whole thing about deterrence rests on the credibility of its use. When people say you’re never going to use the deterrent, what I say is you use the deterrent you know every second of every minute of every day and the purpose of the deterrent is that you don’t have to use it because you successfully deter.
ANDREW MARR: So no point at all in spending billions and billions of pounds if our enemies think we’d never use it?
GENERAL SIR NICHOLAS HOUGHTON: Yeah because deterrence is then completely undermined. And I think people have got to ... You know politic... Most of the politicians I know understand that and I think that, dare I say, the responsibility of power is probably quite a sobering thing and you come to a realisation ‘I understand how this thing works’.
Two points to note.
CDS only stated that he would be worried if the thought that a Prime Minister would not use the nuclear deterrent under any circumstances were publicly stated. He made no reference to Corbyn, simply the public announcement of such a thought. In fact, when Marr tried to tie CDS's response specifically to Corbyn, CDS dismissed the premise, quite rightly, by saying that "there’s a couple of hurdles to cross before we get to that." His reply referred to the thought declared publicly, nothing to do with Corbyn saying it.
The rest of that part of the interview was explaining why declaring the thought publicly negates the deterrent effect of being a nuclear power and noting that politicians generally get that.
Nowhere in his careful response did CDS ever say, express or hint at any of the following:
Disrespect to the Leader of the Opposition,
Disagreement or disapproval of the Leader of the Opposition's political views nor his intention to scrap or undermine the UK's nuclear deterrent,
Morale in the Armed Forces,
Judge Corbyn's suitability to become Prime Minister,
"Answer a specific question relating to the Leader of Her Majesty's Opposition's previously expressed distaste of a nuclear deterrent" (he commented ONLY about his worry about the public expression of such a thought,
Use the Andrew Marr programme as any kind of platform.
I highly recommend to those that are so outraged by your own perception that this is a military leader making political comment that you go and find the transcripts of more of Marr's programmes and then think a little more. You may just find that you have been induced to react by Corbyn's embarrassment at his own folly and by some press sensationalism that followed.
As to continuing conspiracy theories about a mythical BBC agenda, to those that still think the Board push people out for political reasons, just look at the very wide (political and social) range of programmes the Corporation airs, many not actually made by the BBC and many that are totally opposed to your supposed BBC stance.