May 7, 2015 9:58 AM EDT

Sofia Vergara and Nick Loeb squared off on the morning talk shows Thursday in their battle over their frozen embryos – with the Modern Family actress labeling her ex-fiancé an opportunist and Loeb claiming he just wants protect two lives that “have already been created.”

Vergara, 42, told Good Morning America that the embryos are a non-story, legally speaking, and she criticized Loeb, 39 – and the press – for bringing a private matter into the public eye.

“I’ve been working very hard for 20 years to get to this point where I am,” she said. “I promote all my movies, all my work, but I don’t like promoting my private life. And I don’t want to allow this person to take more advantage of my career and try to promote himself and get press for this.”

She seemed dumbfounded about why Loeb is getting any press – much less a New York Times op-ed – about the matter. The two signed an agreement, after all, that both must consent in order to bring to term the embryos they created together when they were a couple in 2013.

“Why is the press allowing somebody to invent things and create press for himself?” she asked. “He’s not an actor. He’s not a celebrity. It’s like, why?”

She added: “This shouldn’t be out there for people to give their opinion when there’s nothing to talk about. There’s papers signed … I don’t understand why the media is allowing a person to just try to put me down, and make it like something is happening when nothing is happening.”

On Today, meanwhile, Loeb said he never believed Vergara “was going to change her mind” about the embryos, and that he’d be happy to raise the kids as a single father.

“It has nothing to do with whether it’s her baby or a baby,” he said. “Lives were already created … I wouldn’t toss them aside.”

He’s not asking Vergara to take financial responsibility for the children, he added. “I’ve offered to her to waive all financial responsibilities,” he said. “I want these children to have the best lives possible … There’s nothing more that I want to do than bring these children to life.”

In closing, both of them claimed they’re not overly bitter about what’s happening.

“I think Sofia is a wonderful, wonderful woman,” Loeb said. “I don’t hate her at all.”

For her part, Vergara mentioned how happy she is with Joe Manganiello, and how blessed she is to have such a successful career. “I’m not sad. I’m grateful,” she said. “I have to enjoy what I’m living right now.”

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