Democratic Alliance (DA) leader Helen Zille named a shadow Cabinet for the national government on Thursday, saying the party would never buckle to a "narrative" on gender quotas.

In naming the cabinet, Zille, who has been involved in a verbal fight with the African National Congress (ANC) over her all-male executive in the Western Cape, said quotas had nothing to do with gender issues in South Africa.

"In everything we do we focus on the fitness for positions," she said at a press conference at the DA's offices in Parliament.

"We had to look at preferences, abilities and other duties in the party.

"We have named a shadow Cabinet because we want one-on-one correspondence between the government and the opposition."

Zille said a "narrative" existed in South Africa that quotas took precedence over all other considerations. Women still faced issues such as gender violence and single parent families, she said.

"This is not the DA's narrative. It has nothing to with the real oppression of women in South Africa. It has nothing to do with gender equity and the advancement of women. It has to do with women who are owed political favours."

Zille named the DA's leader in Parliament, Athol Trollip, to be the shadow minister for the Presidency.

Dion George will shadow the Minister of Finance, Dianne Kohler Barnard, the Minister of Police, Juanita Terblanche, the Minister of Home Affairs, Dene Smuts, the Minister for Justice and Constitutional Development and Kenneth Mubu, the Minister of International Relations and Co-operation.

Ryan Coetzee will be the shadow minister of Economic Development.

"The people who are here are here because they want to work, not because they want pomp and ceremony and status," Zille said.

Zille said the pillars the party would focus on would be State justice, education and health.

"The criminal justice system, education and health care are the pillars on which society is built," she said.

Zille has been involved in a spat with the ANC Youth League (ANCYL) in the past week after claiming President Jacob Zuma was a womaniser who had put his wives at risk of contracting HIV.

She had been responding to criticism from the ANC on her all-male executive.

The ANCYL, in response, accused Zille of keeping concubines and having sex with her all-male provincial executive council.