His button is very big and powerful
The administration's decision to withdraw from the INF treaty isn't surprising since John Bolton is the National Security Adviser. He doesn't believe in arms control of any kind. He apparently thinks that nuclear war is winnable. But it's also the case that Russia has long wanted the US to withdraw so they could continue to develop these medium range nuclear weapons without having to pretend that they aren't:
The article linked is from 2007. This isn't a recent goal. The Washington Post shows here what Putin has been saying about this as recently as 2016:
In a  exchange captured by a Kremlin transcript, Putin called the leaders of the Soviet Union who forged the treaty with the United States in the late 1980s “naive” for its terms (emphasis added):
Q: Does Russia see any value in this treaty, and if yes, then what exactly? Is it even worthwhile to be part of this treaty?
PUTIN: It would be of great value to us, if other countries followed Russia and the United States. Here’s what we have: the naive former Russian leadership went ahead and eliminated intermediate-range land-based missiles. The Americans eliminated their Pershing missiles, while we scrapped the SS-20 missiles. There was a tragic event associated with this when the chief designer of these systems committed suicide believing that it was a betrayal of national interests and unilateral disarmament.
Why unilateral? Because under that treaty we eliminated our ground complex, but the treaty did not include medium-range sea- and air-based missiles. Air- and sea-based missiles were not affected by it. The Soviet Union simply did not have them, while the United States kept them in service.
What we ultimately got was a clear imbalance: the United States has kept its medium-range missiles. It does not matter whether they are based at sea, in the air, or on land; however, the Soviet Union was simply left without this type of weapons. Almost all of our neighbours make such weapons, including the countries to the east of our borders, and Middle Eastern countries as well, whereas none of the countries sharing borders with the United States, neither Canada nor Mexico, manufacture such weapons. So, for us it is a special test, but nevertheless we believe it is necessary to honour this treaty. All the more so since, as you may be aware, we now also have medium-range sea- and air-based missiles.
That doesn’t sound like someone who will be particularly unhappy without the treaty — which he argued was stacked against his country to begin with.
So, for all the fatuous nonsense we've heard over the past day about Trump standing up to the Russians, let's just say that this happens to be a situation where Bolton and Putin see eye to eye and the president is able to please both the Russia hawks and his handler at the saem time. Win-win.
Charlie Pierce gets into the history on this:
I'm not sure how giving Vladimir Putin everything he wants is supposed to hurt him, but I am not the Secretary of State. This is an odds-on decision to start another nuclear arms race in Europe, which can only hype up the ambitious Russian ganglord's dreams of a gangster-capitalist new USSR. The INF Treaty was one of the Reagan Administration's shining accomplishments, and one of the first indications that Mikhail Gorbachev was a real reformer.
It was the first arms-control agreement that required a reduction in nuclear weapons rather than simply freezing the number of them in place. It brought Europe out from under a dark shadow. (These were the days in which nuclear war was again thought to be feasible, if not imminent.) It allowed people in Europe to breathe a little easier. For all his faults, Reagan made the INF Treaty a landmark in nuclear diplomacy, and it led directly to President George H.W. Bush's START treaty which cut in half the nuclear arsenals of both countries. Whereupon, of course, a short time later, there was no Soviet Union any more. You want my blogger's guess? The START agreement is due to expire in 2021. That will be the next target for this administration*'s reckless vandalism, if this president* were to be re-elected.
If your partner in a treaty cheats, you use the mechanisms of the treaty to hold the partner to account. You don't simply abandon the treaty—unless, of course, you want to start arming up in Europe all over again and (maybe) don't mind much if Russia does the same thing. Were I an ordinary Czech, say, I might wonder if two oligarchs weren't actually working together to dominate the European landscape. Several months ago, arms-control expert Joseph Cirincione made this very point when the idea of abandoning the INF agreement was first floated.
Maybe that is why no one wants them. No government in Europe or Asia is calling for these weapons or offering to host them. In the 1980s, deployments of nuclear weapons into Europe brought millions of Europeans into the streets in sustained protests. This time, the decision to pull down yet another security pillar in the trans-Atlantic alliance will deepen an already growing divide. “Of course, it will widen the rift between Europe and America,” former British diplomat and director of the European Leadership Network Adam Thomson told me this week, “European governments will look even more intensely at how they can provide for their own security.” It will not be as insulting to European leaders as Trump’s violation of the Iran anti-nuclear deal, he said. Europeans saw that agreement as the crowning achievement of European Union security diplomacy. But it will burn.Cirincione further argued that the real vandal here wasn't Pompeo, but, rather, National Security Adviser John Bolton, a truly bloodthirsty crackpot who'd tear down the entire global political order if it made him feel like Julius Caesar. Cirincione wrote:
Perhaps that is why the decision to jettison the INF Treaty did not come from the State Department (which normally has jurisdiction over treaties), but out of Bolton’s National Security Council. Bolton has an obsession with tearing down the treaties, legal arrangements, and global governance councils created by Republicans and Democrats over the past 70 years. He views treaties as tools of the global Lilliputians to tie down the American Gulliver. Bolton insists that maintaining U.S. global dominance requires that the U.S. have a massive spectrum of conventional and nuclear options. “Violations give America the opportunity to discard obsolete, Cold War-era limits on its own arsenal, and upgrade its military capabilities to match its global responsibilities,“ Bolton wrote with former Deputy Assistant U.S. Attorney General John Yoo.
As for Putin, there's a good chance he pulled Trump's strings in Helsinki:
Trump and Putin, who control the world’s two biggest nuclear arsenals, are due to meet on Monday in Helsinki, a venue which evokes memories of Cold War show-downs between the Soviet Union and the United States.
“The proliferation is a tremendous, I mean to me, it’s the biggest problem in the world, nuclear weapons, biggest problem in the world,” Trump said alongside British Prime Minister Theresa May at her Chequers country residence.
“If we can do something to substantially reduce them, I mean, ideally get rid of them, maybe that’s a dream, but certainly it’s a subject that I’ll be bringing up with him,” Trump said of his upcoming meeting with Putin.
Trump added the nuclear arsenals were “also a very expensive thing but that’s the least important.”
We know Trump doesn't read his briefing papers so we can't expect that he has learned anything about this issue since becoming president. Before that his knowledge of it consisted of bragging that his uncle was a Professor at MIT:
“I had an uncle went to MIT who is a top professor. Dr. John Trump. A genius. It’s in my blood. I’m smart. Great marks. Like really smart...My uncle used to tell me about nuclear before nuclear was nuclear,” said Trump (an impossible feat, since he was born one year after the first nuclear bomb was dropped on Hiroshima in 1945). “He would tell me, ‘There are things that are happening that could be potentially so bad for the world in terms of weaponry.’ He understood, literally, nuclear before it was nuclear.”
This article by David Corn about Trump's musings about nuclear arms will chill you to the bone. This uneducated, delusional narcissist has been blathering incoherently on the subject for decades.
Remember, the reason Rex Tillerson called Trump a moron was over this issue:
President Donald Trump said he wanted what amounted to a nearly tenfold increase in the U.S. nuclear arsenal during a gathering this past summer of the nation’s highest-ranking national security leaders, according to three officials who were in the room.
Trump’s comments, the officials said, came in response to a briefing slide he was shown that charted the steady reduction of U.S. nuclear weapons since the late 1960s. Trump indicated he wanted a bigger stockpile, not the bottom position on that downward-sloping curve.
President Putin sees that he's dealing with a president who has the mind of a child. So does Bolton. But as Charlie Pierce pointed out, these two motives are going to come into direct at some point:
If Putin lards up his western frontier with new generations of intermediate missiles, what will this administration*'s response? Bolton will want to arm up in equal measure. The president*'s truckling to the Russian president will collide with that. What does Bolton think the "global responsibilities" of the United States actually are? Can't anyone here play this game? Which way to the basement?
I think both Putin and Bolton think they control Trump. This issue counts as a win for both. But I'd be prepared to bet that only the first one really has Trump's number.