The natural answer is simply that they're hopping onto a bandwagon. They've discovered that sport is popular, and want now to be associated with it - notwithstanding that they cut the schools sports partnership only a few months ago.
There are other possibilities. One, pointed out by Shuggy, is that a sporting career is a suitable ambition for the lower orders to have.
Now, you might think this is a knock-down argument for teaching sport. It inculcates non-cognitive skills such as teamwork, discipline and the pursuit of excellence that help people get ahead in later life.
Maybe. But this poses a question: why assume that we need competitive sport to promote these values? The phenomenon of counter-education means many people are turned against sport, and the good values associated with it, by being compelled to do it in schools. For such people, discipline and teamwork might be better instilled by encouraging non-sporty types to join choirs, bands or dance troupes.
Why, then, want sport to be taught in schools whilst sneering at Indian dancing?
The answer, I think, lies in a paper (pdf) by Jeremy Celse.He points out that sport doesn't just promote virtues. It also promotes the vice of envy. It encourages people to become more cut-throat and more willing to hurt others to get ahead.The sporting mentality, remember, gives us Kevin Pietersen and John Terry as well as Mo Farah.
And herein, I think, lies Cameron and Johnson's enthusiasm for teaching competitive sport. They want schools to produce the right sort of chap - people like themselves.And this requires that they churn out ruthless competitive egotists.