Styles' fans quickly jumped to his defence, condemning the political commentator.
Its most-liked response, from actress and filmmaker Olivia Wilde, has over 110,000 likes, and reads: "You're pathetic."
But Owens, who previously served as the communications director for the right-leaning Turning Point USA and is a supporter of President Donald Trump, said she refuses to apologise.
"Since I'm trending I'd like to clarify what I meant when I said 'bring back manly men.' I meant: Bring back manly men. Terms like 'toxic masculinity' were created by toxic females. Real women don't do fake feminism. Sorry I'm not sorry."
Other fans echoed Wilde's tweet, saying they didn't buy the old fashioned ideas about what made someone masculine.
"Harry Styles is manly in ways that matter. He's manly in the way he respects women. He's manly in the way he is kind. He's manly in that he doesn't have to belittle others to lift himself up. We need more men like him in our world," one Twitter user wrote.
In Styles' accompanying article in Vogue, he describes good clothes as being "like a superhero outfit".
"Clothes are there to have fun with and experiment with and play with," Styles said.
"Once you remove any barriers, obviously you open up the arena in which you can play. I'll go in shops sometimes, and I just find myself looking at the women's clothes thinking they're amazing."
