NATO was set up to confront the Soviets and prevent the Communist superpower advancing West. Stalin had managed to occupy and retain half Germany and all of Eastern Europe at the end of WWII. When the Soviet Union collapsed, its own defence treaty organisation collapsed too. The Warsaw Pact was disbanded.
NATO was designed to deter and defend, not to frighten and provoke. The Warsaw Pact was an instrument of conquest. So when it was disbanded it might have been best to disband NATO. But no, too many general’s careers and defence contracts would have gone up in smoke, so it was decided to keep it going to counter anything happening in the world which nominally threatened its members. New threats did develop and engagement in the Balkans, Afghanistan and Libya followed and, notably, Iraq One but not Iraq Two.
Unfortunately NATO, in a rather triumphalist mood, expanded East, absorbing several ex WP members, until almost at the Russian border. This both threatened and provoked and Russia has been a troublesome partner on the world stage as a consequence. The mistake was not to recognise that with the fall of the Berlin Wall, all Europe was now one and Russia was in fact a European power. There were just two options for a secure outcome. Disband NATO when the Warsaw Pact fell, or keep it going, but with Russia in it. A third option was to keep it going and exclude Russia. That was the one chosen. Now the challenge is to clear up the mess resulting.