TL;DR: it wasn't because he wanted to attack Communist China (and nukes would have been needed for his proposal), it was because he undercut government foreign policy and defied orders in publicly advocating for it.

"It was simply, as General Marshall pointed out in his testimony before the Senate Committee, the situation of a local Theater Commander publicly expressing his disagreement with a policy which superior authority had repeatedly communicated to him in the clearest terms." (emphasis added) Matthew Ridgway, The Korean War, near the start of chapter 6. (Since Ridgway was MacArthur's successor, you might suspect bias, but he certain comes across as evenhanded and does praise MacArthur in many areas, and this account agrees with others I've seen.)

I added the emphasis because the real problem was "publicly", as General Marshall pointed out in his testimony.

As for what his disagreement was:

What he did argue for earnestly and continually was the use of our great sea and air power to isolate Communist China and to destroy 'for a generation' her potential for armed aggression.

Destroy their airbases in Manchuria. Blockade. Destroy their industry. Support Chiang's invasion of the mainland. (Use Chiang's troops in Korea too.)

He wrote off Europe and so he didn't worry that it would bring in the Soviet Union, and didn't think that the USSR would intervene anyway. If they did, good: they were growing in strength, so it would be better to take them on sooner than later. ".... his ultimate aim, the destruction of Communism throughout the world by theuse of armed force."

The ideas were considered in Washington and ruled against on the obvious grounds. Nuclear war was considered as entirely possible.

One of the proximate causes was MacArthur issuing a public statement around 23 or 24 March 1951 that uncut -- gutted -- a statement being prepared by the State Department, and in open defiance of Truman's order of 6 December 1950 requiring all officials "to abstain from any declarations on foreign policy". (Which they shouldn't be doing anyway.) There were other incidents of communications private and public.

I should have thought to search first. Let me point to How close was Douglas MacArthur to actually nuking North Korea.. /u/ivymikey wrote:

Not close at all. MacArthur pushed to use nuclear weapons, but this was a strategic ploy. He wanted the Chinese (and, to a lesser extent, the USSR) to fear nuclear war. However, while MacArthur, as commander of the Far East, had nuclear bombs in Guam, they did NOT have their nuclear cores, which were in the mainland US, under the control of Atomic Energy Commission.

In April of 1951, 9 fully armed nuclear weapons WERE available in Guam, but MacArthur had been replaced by Matthew Ridgeway at that point. Ridgeway was given permission to use nuclear weapons at his discretion, but at that point, the war had already been fought to a stalemate and armistice talks would officially begin in July.

How could it be a ploy if the threat of nuclear weapons was only communicated inside but not to the Chinese? I have the impression that anyone advocating or considering expanding the war to China understood that they would have had to use nuclear weapons. Leaving aside the size of China, the US didn't have anything near World War II levels of conventional strategic bombers.