Story highlights Earlier in the day, Melania Trump said she'd work to improve a social media culture as first lady

"Doesn't this start at home?" Cooper asked Conway

(CNN) CNN's Anderson Cooper questioned Donald Trump campaign manager Kellyanne Conway Thursday on how Melania Trump could crusade against online bullying when her husband famously antagonizes others on Twitter.

Earlier in the day, Melania Trump, in her first speech on the 2016 trail , said she'd work to improve a social media culture that she said has gotten "too mean and too tough" if she became first lady.

"Doesn't this start at home?" Cooper asked Conway on "Anderson Cooper 360." "Isn't the problem at her own dinner table?"

"No, it's not at her own dinner table," Conway fired back. "The fact that her husband is running for president and defends himself sometimes or tweets things out --"

"Talking about Carly Fiorina's face wasn't a counterattack. That was just an attack," Cooper interjected. He was referring to Trump's attack on the former Hewlett Packard CEO and Republican presidential hopeful in September 2015 when he said "Look at that face! Would anyone vote for that? Can you imagine that, the face of our next president?"

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