But viewers watching at home appeared unconvinced by her argument, with one tweeting: "She's effectively saying that manners and discipline have no place in the home."
Many others disagreed with the suggestion that parents should teach their children about using bad language.
"Unbelievable that we are discussing should kids be swearing at home absolutely horrific," fumed one person.
Another said: "This woman saying that children should be allowed to swear encapsulates why kids are so messed up these days. She's effectively saying that manners and discipline have no place in the home."
"Children should not be 'encouraged' to swear but... Monkey see, monkey do. You can protect kids from so many things but you can't protect them from life," reasoned one.
Ahead of the segment a reporter had interviewed families for their take on attitudes towards swearing.
One father said: "I don't think it's good parenting to let your kids swear."
His daughter added: "They could affect other people's feelings. I don't swear."
One child said it wasn't worth the punishment, as he wouldn't be allowed to play on his games console.
Another father holding his young daughter said: "I just don't think if she's swearing it's going to be good for her social connections."
Dr Byrne said it struck her how concerned the parents were about the negative social connotations swearing had, but said it was important for children to have an understanding of words' impact.
"One of the good things that came from those interviews is the little girl who said you have to think about people's feelings.
"If we don't talk about it [swearing] with our kids and they learn swearing just from their classmates on the playground, they're not going to have a sense of how swearing affects people's feelings.
"But also how swearing isn't directly correlated with being awful to people. There are ways to be really vile without using a swear word."
Presenter and life coach Anna Williamson disagreed with the suggestion that children should be taught when to swear as she believed there were no guarantees how well it would be executed.
"People take offense to it. Swearing is not socially acceptable. There's a reason we can't swear on live TV and it's because it does offend.
"That is what is key, it's about creating those boundaries particularly in our children.
"I do get the point about educating but I don't think using swearing liberally is saying it's OK to use it in those circumstances, because I just think it confuses children."