Envy is not selfishness. Selfishness is the desire to have more, regardless of the welfare of others. Envy is the desire for someone else to have less, even if it does not make you better off.

Capitalism is based on selfishness. This is not what capitalism is about, it just tends to come with the turf - it's just that the model deals with. Selfish behavior of individuals will not cause a capitalist economy to fail. If many (or all) people also show compassion towards others, it still works.

Communism is based on trying to combat selfishness. However, even with enormous well meaning education and reprogramming, selfishness still exists, and selfishness causes communism to fail.

Communists are generally envious people. This is not what communism is about - it's just that envious people who want others to have less are attracted to the communist philosophy. It provides a philosophical justification to force others to have less, even if it doesn't actually help anyone. And this is pretty much what communism produces - mass poverty and hardship (except for the elites).

The phrase which best describes envy is 'shoot the cow' (ie, if someone else has a cow and you don't, then shoot it to make you equal).