RHONY Alum Bethenny Frankel Responds to Accusations of Transphobia: 'I'm Not Afraid of Cancelation'

Dimitrios Kambouris/Getty Bethenny Frankel

Bethenny Frankel is facing accusations of transphobia following a discussion she had on her podcast about pronouns and gender identity.

In last week's episode of the podcast Just B with Bethenny Frankel, the Real Housewives of New York City alum, 50, brought up pronouns in reference to 11-year-old daughter Bryn and her school.

"We have to go into the fact that I did a Zoom for my daughter's school and [had] the pronouns conversation with each teacher, each parent, each child," she said. "And my daughter says in school, too, that everybody has to say their pronouns."

"And my daughter didn't even know what hers were, and I can't even blame [her], I know what I am or what I think I am, but I have never said it out loud — it hasn't come up for me — and so she said she didn't know exactly how to say it, someone said it before her," Frankel continued.

Bethenny Frankel/instagram Bethenny Frankel with daughter Bryn

RELATED: Jagged Little Pill Star Antonio Cipriano Exits Show After Producers Were Accused of Transphobia

The Skinnygirl mogul then launched into a conversation about stories she has heard about sleepaway camps over the summer, noting that Bryn did not attend any.

"It's an all-girls camp and a person with a penis, who identifies as being a girl, went to the camp and was in the bunk with the girls. And the girls saw her — because it's her, because it's a male anatomy but identifying as a woman — so the other girls saw a penis," she said.

Frankel said "the parents obviously weren't that happy" and added that she heard "this girl with a penis was making out with a lot of different girls at the camp."

She also commented on trans athletes competing in sports, questioning whether it is "fair" and suggesting that the sports be graded "on a curve." (Recent research has shown that there is no scientific case for excluding trans girls from girls' sports)

Frankel additionally implied that gender and sexual identity could just be a "phase."

Cindy Ord/Getty Images Cindy Ord/Getty Images

RELATED: Bethenny Frankel Denies Potential RHONY Return: 'I Haven't Spoken to Bravo Since Leaving'

She later noted that Bryn is "amazing" when it comes to the topic of gender identity.

"My daughter understands all of this, it's amazing, they have different language, different understandings, but she also hasn't seen a penis. So, in a camp, she'd see girl parts so I think these conversations are also fluid," she said.

Addressing the reality star's comments about pronouns, Human Rights Campaign's Senior Vice President, Programs, Research & Training Jay Brown tells PEOPLE statements like Frankel's can be harmful.

"Transgender people, and transgender kids, are exactly who we say we are — and using our correct pronouns is pretty basic way of affirming who we are. Imagine someone calling you by the wrong name or pronoun," Brown tells PEOPLE. "For folks who haven't ever had to think about this, the act of introducing oneself with a pronoun can be curious. But most folks come to understand the value."

"People in power -- whether it's a reality TV star or legislators in statehouses across the country --who use their platforms to mock trans youth should know that it's incredibly harmful. It can have devastating effects on the mental health of those most vulnerable among us. Trans kids should be affirmed and supported."

Never miss a story — sign up for PEOPLE's free daily newsletter to stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human interest stories.

After the Bravo star was sharply criticized on social media for the offensive comments, she doubled down on what she said.

"I was absolutely not wrong. And I'm going to discuss this again this week. Thankfully I have a platform to clarify what the media loves to distort. @justbpodcast ps. I'm not afraid of cancelation so not afraid of charged discussions," she wrote on Twitter in reply to a listener who shared, "This is a time to learn, Bethenny. Humility can be a good thing. Doesn't mean you're weak. You were wrong with your comments."

When Frankel wrote "@PageSix says I'm transphobic so it must be true…" another fan responded, "B not a good way to apologize. Your intro to the podcast WAS offensive. Let's learn something here."

"Not apologizing….so don't hold your breath," she wrote. "I didn't do a single thing wrong. People need to be able to have discussions without fearing the cancelation citations you get excited to give. Wrong celeb. Find someone afraid to troll."

One social media user, who identified themselves as a member of the LGBTQ+ community, said Frankel's "transphobic" words did "damage."

"I didn't do one thing wrong," the Big Shot with Bethenny star then said. "Conversations are healthy. Try it. Doubling down. I'm not a celeb who panics in fear of cancelation Bc I didn't say something precisely how you needed to hear it. I don't have a transphobic bone on my body so take it elsewhere. Watch handmaids tale."

"You are a straight woman, I am a gay woman," the same user replied. "How about YOU try having a conversation about why your words were extremely hurtful. I have tweeted you many times thanking you for your humanitarian work. You missed the mark on this. Admit it, learn and try harder. Like we all do."