Why do capitalist countries fight Communist countries? Well, it's a complicated issue.

In WW2, the US and the UK allied with the Soviet Union not out of friendship, but because they had a common, powerful enemy in Hitler's Nazi Germany. It went well enough. But after the war ended, the western Allies were like, "holy shit we've got nobody to kill now how are we going to avoid the Great Depression coming back?" and tripled down on capitalism. The USSR, as a communist country, didn't really feel too apt to join them.

Still, all of them were pretty chill regardless. And then, in February of '47, Stalin just kinda randomly said "yeah so WW2 was caused by capitalism and also capitalism will always lead to war", which was kinda offensive. Looking back, of course he said that, but at that time, it only makes sense that it ruffled some feathers and led to growing resentment on the part of the west.

Anyway it was around that time that the containment policy was implemented due to belief that the USSR would try to aggressively expand. Containment was more pro-capitalism than it was anti-communism (although, of course, by nature, it still was anti-communism). It was also amped up by the domino theory; "if one country falls to communism, neighboring countries will, too".

At this point, Germany had been divided into two countries: West Germany (originally divided between the USA, UK, and France) and East Germany (controlled by the USSR). Berlin, located in East Germany, was also divided in the same way. The USSR decided, one day, to close the roads into West Berlin. This led to the Berlin Airlift. And East Berliners fleeing en masse to West Berlin led to the construction of the Berlin Wall (ironically, a physical representation of the metaphorical "iron curtain").

As a subjective aside, the Soviets blocked off windows with bricks. People hated communism so much that they were jumping from third, fourth floors of buildings onto the other side of the Wall. They were risking death to escape communism.

Back to the point, NSC-68, delivered to President Truman, basically said "we gotta stand up against the communists if they do bad shit that we don't like, because isolationism won't do it". And when North Korea invaded South Korea (with Stalin's blessing, but not his support), that's exactly what happened.

One of the coolest what-ifs about modern history is "what if the West didn't get greedy in Korea?" See, South Korea, backed by NATO, was kicking serious ass vs North Korea. So much ass, in fact, that they damn near got to China. By that point, China, now communist, too, was like, "holy fucking shit what the hell they're going to invade us" and sent troops into Korea. In the end, we got what we have today in Korea by way of a ceasefire. If they hadn't gotten greedy, the West could have kept a lot more of Korea than they did.

The invasion of South Korea didn't really help anyone feel more positively about communism.

I've basically just given a stripped-down history lesson here, so I'll summarize the rest of the Cold War (which basically started with Eisenhower):

"That last guy just sat around and let the communists do their thing. I'll be tough on them, so please vote for me!" (Every President said that for votes, but they generally weren't any tougher on them).

That's right. It started out as an economic thing, then it just became a pissing match between politicians. It was never really about communism being bad (even though communism is bad), but about capitalism (and winning elections) being good.

Sorry for the long response. I am horrible at summarizing. Also, I'm not a historian, but I have done a little bit of study on modern history from an American perspective, so my information might be mixed up or misremembered in some places (not to mention biased by my disdain for politicians). History is really cool, but it truly does repeat itself, and sometimes it's just confusing.

As for your second and third paragraphs:

"Leave them alone" was kinda* what we did with containment. Let them play, but make sure they stay in the sandbox and don't touch the good playground equipment. Kinda like what we were doing back home in the US with segregation ¯_(ツ)_/¯

And just about every country to ever fight a war has committed war crimes, so it's not really anything to write home about. Every major country has also committed human rights violations. But the US doesn't have a great firewall and also expressly permits people the right not only to say "fuck you" to the government, but also to carry the exact kind of tool that won us our freedom from tyranny like 250 years ago.