The EFF stormed out of the National Assembly on Thursday before the nomination process began for a new president of South Africa.
The party alleged that Parliament was "an illegitimate structure", because the Constitutional Court found that it had failed to hold Zuma to account during his presidency. The EFF and the DA are pushing for Parliament to be dissolved and early elections held.
The EFF refused to take part in the nomination process, and walked out before newly elected president Cyril Ramaphosa was voted in. The party came under fire on Twitter for its decision to walk out – even from its own supporters.
Independent political analyst Molifi Tshabala that while there is a cloud hanging over the legitimacy of Parliament, the EFF's agenda may have been to delegitimise the Ramaphosa presidency.
"The EFF may also be [worried about being] seen as betraying their working-class support base by going along with a populist Ramaphosa campaign. Ramaphosa is seen ... as a capitalist. But the EFF did say [that] they would give Ramaphosa the chance to deliver the state of the nation address uninterrupted," Tshabalala said.
"The EFF's problem is not with Zuma or Ramaphosa – it is with the ANC as a whole. Walkouts are something we may come to expect, because of clashing ideological views."
The University of Johannesburg's professor Mcebisi Ndletyana said the EFF's walkout on Thursday was a "risky calculation".
"They are raising a good point – that Parliament did not exercise its responsibilities [to hold] Zuma to account, and the same Parliament is now electing one of its own to replace him. What sanctions should be brought against Parliament? They believe Parliament should be dissolved. It is arguably a legitimate demand," Ndletyana said.
"But the unhappiness over their strategy has to do with the excitement that has greeted Ramaphosa's presidency. People are looking and hoping for the return of good days. The question now, is how to do the EFF adapt to a period that is yearning for stability?"
Ndletyana said the EFF's actions arise from an ideological standpoint.
"A walkout depends on the gripe. In Zuma's case, it was understandable. But then if you walk out from a legitimate process, it may work against you. The value of a walkout is contextual. The EFF will need to learn where the value is."