When I was a schoolboy in Africa we would play word games aimed to trick other boys into saying something self-incriminating. You might invite your intended victim to repeat the word “ink” followed by the word “iced”, faster and faster until he realised (to mocking howls) that he was saying “I stink, I stink, I stink”. A more savage variant involved requesting an Afrikaner to say “choose my lace” in Afrikaans – with a result too appalling to print.

A means of playing such games at the Commons dispatch box has still to be devised; but, with ingenuity, someone may yet manage to persuade the Prime Minister to repeat the words “up”, “eyes” and “crude”, in that order, as fast as he can. The sound of Gordon Brown apparently declaring “I screwed up! I screwed up!” would bring screams of delight and a ripple of national pleasure.

For a cruel sport is emerging at Commons questions and in media interviews. It’s called Making Brown Say It. The sport is sadistic because the things people want to make the Prime Minister say are not in themselves new or interesting. They are things known to all but which for some baffling reason Gordon Brown himself finds it extraordinarily difficult to say. Making him say them becomes the challenge; watching him wriggle the reward.

It all started last October when, conscious that he lacked a personal mandate and that the polls suggested he could win a snap general election, Mr Brown made plans – then shelved them when opportunistic Tory promises undermined his confidence of victory. There is embarrassment but no disgrace in conceding that you don’t call an election when your opponents may steal the victory, and few sentient Labour MPs saw much problem in admitting as much.

But would the Prime Minister? Somehow he just couldn’t. Sniffing blood, journalists then invited him to deny, “hand on heart”, that falling poll ratings had influenced his decision. Thus cornered, he did deny it. David Cameron skewered him with the same question; and again he was unwilling to acknowledge reality. This made him look idiotic.

Since then the list of mistakes and misfortunes that Mr Brown won’t acknowledge has grown too tedious to detail. Northern Rock, a range of tax twists and U-turns, the recent notorious abolition of the 10p tax rate (where Brown still fails to use the word “I” when acknowledging mistakes) . . . the instances are various. But they have one feature in common. Study his phraseology as a psychotherapist rather than a student of policy might, and this leaps out at you. What Brown really, really, won’t say is that he has been pressured by anyone else into doing anything he did not want to do in the first place; or that on any central question it is his own judgment that has been wrong.

Pressed, he will allow that circumstances have changed and decisions varied or revisited in light of the new situation. Pressed further he will admit that mistakes “were made” or that “we” made mistakes. Pressed even harder he will even use the “I” word and admit to failures of diplomacy, tact, consultation or explanation. But what he cannot allow is either that he has been pushed around, or that a big decision was wrong at the time he took it.

This twin refusal, like the two arms of a nutcracker, puts a man under intolerable pressure. If you can admit you’re wrong, then you don’t need to admit to being pushed by others, but only by your own intelligence, to alter course. If you can admit to being pushed by others you don’t need to admit you were ever wrong: you’ve altered course for collegiate reasons, against your best judgment. But if you are to insist both that your first decision was right, and that your second thoughts do not arise from arm-twisting, you get into an awful tangle when challenged to explain your change of mind.

It was in just such a tangle that Gordon Brown faced John Humphrys on the Today programme and Adam Boulton on Sky News on Thursday. He will have known he would face questions about Alistair Darling’s Budget U-turn, raising the tax threshold to compensate for pain inflicted by abolishing the 10p rate.

How would he reply? By saying he should never have invented the 10p rate? Or never have abolished it? Or would he say that this week’s policy shift would not have been his preference, but it was affordable, and he was therefore bowing to parliamentary anxiety and national concern?

To my incredulity, he told his interviewers that the £2.7 billion tax cut, financed by borrowing, was a response to the world economic downturn: a measure to stimulate domestic growth by putting extra money in people’s pockets. Brown said he wanted to ease the financial squeeze being faced by hard-working families. Asked why the need for this had only been discovered since the Budget, he could give no answer. It was pitiable.

It was also scary. I’ll tell you what scares me, and scares (I believe) a wider public who may not always be consciously aware why. It’s not the thought that the Prime Minister may be lying. It’s a more disturbing thought: that he may not. That under the terrible internal pressure created in his own head by a refusal to accept either that his will may be thwarted or his judgment questioned, the PM is having to warp the external world to make it fit.

Could it be that it is to himself, and not to us, that Mr Brown is unable to acknowledge reality? That he really doesn’t now think he did change his mind about that snap election for fear of losing it? That the main reason for a Budget U-turn was a need he suddenly saw for economic stimulus? That Wendy Alexander was not calling for an earlier referendum on Scottish independence? That the May local and mayoral elections were not a tremendous rebuke to his administration?

We expect politicians to lie. We don’t like it but we understand it. Caught between the world as it is and the world politicians keep promising to make for us, we do see what drives them to misrepresent the world, rewrite the promise, or both.

Conversation between the public and our politicians is eased by the half-intended, half-acknowledged wink. And if in their kiss-and-tell diaries politicians later paint a picture of private sniggers and sneaky lies, it’s almost reassuring. At least it suggests that if the covers come off we’d all agree on what we see. When a man blushes, something is shared.

But a cold, angry repudiation of the evidence itself, a look that suggests a different prism, a different picture; a strange, knotted, jaw-clenching, fact-defying, interview-wrecking rejection of what the rest of us see plain as daylight . . . this disturbs more deeply than everyday mendacity ever can. Where could a national conversation with such a man begin?

Times Recommends

• Graveyard of empires could claim more careers
• Would you live on the wrong side of the Berlin Wall?
• At last we’re getting our heads out of the sand