It would be tempting – and wrong – to cast President Barack Obama's decision to cancel a one-on-one summit with President Vladimir Putin during his forthcoming G20 visit to St Petersburg exclusively in terms of America's frustration at Russia's decision to grant temporary asylum to Edward Snowden.

That is, of course, how the Kremlin's ever loyal media will try to frame it – ignoring the fact that the Russia in which they live treats its own dissidents with a vindictiveness unseen for many decades. The deeper reason behind such a public rebuff is one that the Russian foreign policy establishment will find less easy to explain away.

While Putin considers himself the elder statesmen of such international gatherings, most of his former cronies on the international scene are yesterday's men. Only Silvio Berlusconi limps on, still a senator and party leader for the time being, but his star is not exactly shining at the moment. These days, Putin is not treated abroad with the respect he thinks his political longevity deserves.

The last occasion to measure this was his trip to Hanover in April, where his German interlocutors, bristling with the fury over moves by Russian authorities to confiscate data from German-financed organisations working in Russia, gave the Russian leader in private a piece of their mind. Contrast that to the time when Putin, informed of Angela Merkel's fear of dogs, made sure his pet labrador was in the room when they met. Merkel no longer feels she has to court Russia.

And neither, apparently, does Obama.

This is Putin's loss, because the architect of the "reset" policy to re-engage with Russia, Michael McFaul, who is now the US ambassador in Moscow, privately agrees that the policy he worked so hard on is now dead. The wording of the White House statement to postpone the summit is relevant in this regard.

It speaks of a lack of progress on missile defence, arms control, trade and commercial relations, global security issues, human rights and civil society … the blockage extends right across the whole spectrum of the relationship defined by the so-called reset. While few expected much progress to be made in any of those fields, the existence of joint committees and regular meetings maintained an illusion of strategic relationship.

The reset has brought concrete benefits to the US, not least the transit of thousands of US troops over Russian airspace to the airbase it leases in Manas in Kyrgyzstan (and then onto Afghanistan). Few pragmatists in the world of foreign policy treat the reset's demise with any glee. But if Obama is a president who wants to concentrate on those policy areas he can personally affect, his impatience with Putin says a lot about where the US thinks that relationship is headed.

The decision to forgo the summit is a blow aimed at Putin personally. It deprives the Russian leader of a valuable prop, one that tells his domestic audience it has a world leader who can measure his stature again the biggest and the best.

This summer, if the latest stunt is to be believed, Putin caught a huge pike in Siberia, 46lb in weight. If you were the president of the United States, would you really want to appear in St Petersburg as the latest quarry this big game hunter had caught?