It may not have been the breakup to end all celebrity breakups, but on Tuesday at the Television Critics Association press tour during a session about “The Muppets” when Kermit the Frog acknowledged that “Piggy and I have gone our separate ways,” the news made headlines. The iconic puppet couple later released a joint statement, declaring that “After careful thought, consideration and considerable squabbling, we have made the difficult decision to terminate our romantic relationship … This is our only comment on this private matter … unless we get the right offer.”

The split is perfect fodder for “The Muppets,” ABC’s forthcoming parody of the reality television and mockumentary genres; it will follow Kermit and other muppets as they work behind the scenes on Miss Piggy’s late-night talk show. (“The Muppet Show” took on then-dominant variety shows when it debuted in 1976.) But the most interesting part of the panel wasn’t the news of the breakup: it was the reminder of just what a cultural force Miss Piggy is. Kermit may be a lovable frog, but it’s his wild, erratic ex-partner who I’m excited to see back on television.

It’s absolutely true, as one reporter at the panel pointed out, that Miss Piggy casts a considerable shadow over pop culture. Her absolute conviction that she’s the most gorgeous, fascinating, talented pig going has long been a considerable force: if you’re skeptical, she’ll win you over or karate-chop you into submission. And she, like Donald Trump, has provided a career for a generation of reality stars whose deluded confidence has an entertainment and business value entirely separate from their actual, often modest, talents. As Miss Piggy herself put it: “It’s very true. Moi has been a role model for a generation of little starlets. All those little starlets that are running around town. Yes, they’ve all modeled themselves after moi.”

But Miss Piggy isn’t merely a wellspring for the kind of reality television stars she’ll soon be parodying. This spring, while accepting an award, she declared that ““Starting today, moi is a feminist!” And while Miss Piggy might have been riffing on the propensity of young starlets to declare themselves new converts to the Church of Steinem, she was also stating a long-standing truth. In all of her immense appetites and conviction that she should get whatever she wants exactly when she wants it, Miss Piggy represents a wild, voracious sort of freedom. Her embrace of the sort of entitlement normally reserved for men is an unruly, defiantly unrespectable feminist act.

But that charming grandiosity makes Miss Piggy a target for deflation as well as a kind of deranged exemplar. BuzzFeed’s Kate Aurthur noted that during the panel, Kermit repeatedly referred to her as a pig, a term that a certain point stopped being purely descriptive and began to feel like a dig.

Bill Prady, a longtime Jim Henson collaborator and the executive producer of “The Muppets” suggested that “Piggy is a remarkable personality. One of the things that we’re hoping to show for the first time in the series is a little bit behind the public persona and behind the mask. We might even get a camera into Piggy’s house in the morning and catch her before she puts on her makeup,” a suggestion that would feel uncomfortably invasive if he was talking about an actual woman, rather than a cloth puppet.

One reporter even asked Piggy whether she’d gotten plastic surgery, and how she avoids looking “porky,” simultaneously a pun and an insult. (Miss Piggy’s response: “Moi is timeless, is ageless. I just decided one morning that I wasn’t going to get any older. It was as simple as that. You should try it.”) The days when a journalist could ask a real live actress about her weight so directly and insultingly are over; now, queries like that have to come dressed up in requests for details about the training regimen a woman’s taken on either post-pregnancy or in the leadup to a new project. But we apparently feel comfortable asking certain things of a cloth puppet that we wouldn’t ask of a real woman.

None of this is to suggest that Miss Piggy is a moral exemplar. I joked to a couple of other critics that — much as reporters ask networks why they feel comfortable working with artists, like Woody Allen and Charlie Sheen, who have checkered records — I was going to ask the ABC president whether he’d considered Miss Piggy’s propensity for violence when thinking about green-lighting “The Muppets.” Miss Piggy is vain; Miss Piggy is impulsive; Miss Piggy is violent; Miss Piggy might even qualify as basic.

But it’s her very extremity that’s a test for the rest of us. Maybe we think that, like Kermit the Frog, who groused and sniped at Miss Piggy through the panel, that we’re the nice, reasonable people trying to ride out a porcine tornado. I wonder, though, if what we’re really feeling is green with envy.