He did accelerate the process. He caused the Soviet Union to spend themselves into oblivion sooner than they would have done on their own. The Strategic Defense Initiative (SDI or for the leftists "Star Wars") had the potential rendering all of the Soviet nukes useless. The Soviet Union scrambled to come up with something like it and spent themselves into oblivion. Basically Reagan was just bluffing with the SDI but as a result ended a miserably oppressive regime. Leftists hate him for that because the Soviet Union was utopia to them.
