Gordon Brown faces the same dilemma that has vexed earlier politicians hoping to raise standards of education in deprived areas.
He refuses to accept that some children should be doomed to fail just because of the circumstances they were born into.
But while everyone would agree with these sentiments, he runs into trouble as soon as he takes the next logical step - which is to insist that schools serving even the poorest estates can and must aim for good results.
We all know that there are schools where the achievement of the average pupil is poor. Their details are published in league tables every year.
If youngsters from deprived areas are ever to enjoy the same opportunities their middle class peers take for granted, these schools must get better results.
To actually come out and say this, however, provokes a storm of protest - protest which cannot be justified.
Schools can never be expected to improve if we pretend that their performance is good enough already.
That doesn't mean that teachers or heads are doing a poor job.
As Mr Brown rightly says, many of the most talented and determined teachers are to be found in inner city skills, helping pupils who arrive with low levels of attainment and motivation.
Their talents are not always reflected in league table ratings. But there is no contradiction between recognising the work they do, and insisting results must improve further.
The Prime Minister is also right to note that these teachers are often working in challenging circumstances. Their job is not easy.
Ministers would point out that they have pledged to help schools and teachers, for example with the creation of a £400 million fund to help schools with poor results. They also recognise that schools alone cannot improve standards - and have attempted, at least, to cajole parents into playing their part.
The Government has predicted that around two thirds of schools with poor exam results will meet the target of 30 per cent of pupils achieving five or more GCSEs at grade C by 2011.
But Mr Brown is right, finally, to insist that those which fail should be transformed - merged with another school, replaced by an academy or simply closed.
The Prime Minister has been heavily criticised, sometimes justifiably, in recent months.
But in his commitment to improving social mobility, he has a cause worth sticking his neck out for.