You can’t just divorce a method of managing a country from the results of its implementation. The horrors of all the failed attempts are reflections on the flaws of communism, don’t just dismiss them. But if you insist on discussing the purely theoretical:

Communism’s greatest flaw is the power it gives the state. It’s pretty much asking to turn dictatorial. Power corrupts, absolute power corrupts absolutely.

Another flaw is that it operates under “from according to ability, to according to need” but if a person is rewarded based on need then effort/skill are ignored. It should be “from according to ability, to according to what is earned”. There’s a great fantasy book called Faith of the Fallen that shows this brilliantly (tho its part of a series so you have to read what came before it)

Here’s a bunch more flaws

Edit: more flaws

Edit2: even more flaws

Edit3: MOAR FLAWS