The advocate asked his daughter where she thought she would end up without qualifications, to which she responded "leader of the DA or the ANC".
While Zuma has said he did not attend school, he has several honorary doctorates. Steenhuisen has a matric.
Last year, Steenhuisen was criticised for his lack of tertiary education after Sowetan's sister publication Sunday Times reported that the DA caucus in the KwaZulu-Natal legislature recommended that only an MP with a university degree be considered for the position of chief whip. He has maintained he didn't need a degree to serve SA.
"I don't have a university degree. I have never pretended to. I enrolled for a BA in politics and law. However, like many South Africans, I never finished it due to financial and work pressures. I am not ashamed of this," he told parliament last year.
Steenhuisen also said he didn't need a degree to see politicians for who they really are. He was referring to the EFF, saying tertiary qualifications didn't prevent the party from allegedly committing crime.