Look let's be rational. There was an arms race at the time.
Sort of. (See below.)
I'm not sure if the schools teach that anymore. But there was.
Neither am I. I'm 55 years old.
Russia tried to one up American with military might all the time.
Actually, the USSR tried to keep up with U.S. military might, not to one up it. I present the 1960 presidential campaign as an illustration. Kennedy spoke of a "missile gap," implying that the U.S. was behind the USSR in nuclear arms, and (of course) blaming the Eisenhower administration for this situation. In fact, however, the missile gap ran some ten to one IN OUR FAVOR.
The Soviets did catch up eventually, but at no time were they ever in a position of clear superiority.
Reagan would answer their challenge and built the American war machine, finally it got to the point that it placed a strain on the socialist economical system the Russians used and had them stretched thin. So they had to back off or face a revolt of the Russian people. Man Reagan kicked the ass of Russia without firing a shot.
This is simply not true. Or most of it isn't. Where you make your mistake is in thinking that the Soviets increased their military spending in response to Reagan's military buildup. They didn't. In fact, once Gorbachev came to power, Soviet military spending went DOWN, not up.
The Soviet people overthrew the system. There were several factors causing this. One is that it was a messed-up system in many ways from the beginning. Another was that the generation which fought World War II got old and died, and was replaced by people who knew nothing firsthand of the struggles of either the Revolution or the Great Patriotic War, and so evaluated the system without those artificial loyalties. A third was that Gorbachev's reforms loosened the government's control over speech and dissent.
But nothing Ronald Reagan did contributed to this process materially in any way. That is pure myth. Really, the only way that his military buildup could have contributed to the fall of the Soviet Union was if we had gone to war with them, and (thank God!) we did not.