"How can someone who has never had firsthand experience with public education understand how it really works?" the governor asked.
"Does that mean that if Governor Herbert doesn't take a bus to work, that he doesn't understand the bus system?" Corroon countered. "It is a ridiculous assertion."
But it's not an altogether unusual one in U.S. politics, where Presidents Barack Obama and Bill Clinton received demerits from public education advocates for sending their children to private schools. (Obama's daughters now go to the same private Sidwell Friends School in Washington, D.C., that Chelsea Clinton attended.)
Does "firsthand experience" as a parent or grandparent really matter in governing public education? Will it make the state's chief executive any more adept at shepherding a $3.4 billion school system that employs nearly 29,000 teachers and instructs 529,000 students?
The Utah Education Association won't say particularly with the political firestorm that flared last week between Herbert and Corroon.
UEA President Sharon Gallagher-Fishbaugh described Corroon's decision to enroll his children in a private school as personal, not as a discussion topic for the teachers union.
Corroon sends his children to the Madeleine Choir School in Salt Lake City.
"We don't want to get into that," said Kory Holdaway, government-relations director for the UEA and a former legislator. "If the governor wants to make that point, it is his point to make. That is a campaign issue, not a policy issue."
What makes Corroon's decision to send his children to a private school particularly intriguing is the fact that he opposes private-school vouchers. It would "dilute" funding for public education, he said.
Herbert, on the other hand, favors vouchers a point Corroon dinged him on, accusing the governor of backing an effort that would take "millions of dollars from public education to fund private schools."
Herbert's campaign said the governor supports opportunities for parental choice, but considers vouchers a "dead issue," one he does not plan to pursue during his administration.
On a pragmatic level, political scientist Quin Monson doesn't see Corroon's pick of a private school as having any impact on his ability to oversee public education.
"It is important symbolically," said Monson, associate director of Brigham Young University's Center for the Study of Elections and Democracy. "But it stops there."
The governor's reasons for raising the private-school question may have more to do with electioneering than with political philosophy.
Not only could the mention of private schools portray Corroon as an elitist, experts say, but it could draw attention to the fact that Corroon doesn't belong to the state's predominant LDS faith. The Madeleine Choir School is a Catholic institution.
The Herbert campaign denies that its message had to do with anything other than education. Not elitism. Not religion.
"The issue was one of education," said Don Olsen, spokesman for the Herbert campaign, "and education only."
And yet, the governor suggested in a Thursday news conference that the education plan put forward by Corroon which would stiffen high school graduation requirements could eliminate electives such as LDS seminary courses.
Matthew Burbank, a political science professor at the University of Utah, said those comments easily could be interpreted as "coded" references to religion.
"If you talk about things like what will happen to seminary education, if you talk about things like sending [children] to a private school and not a public school, those are ways to make the point about who is, or is not, LDS," Burbank said. "It definitely is meant to send an extra message."
It is a "risky" campaign strategy, according to Michael Lyons, a political science professor at Utah State University. If Herbert's comments are perceived as an attack on Corroon's Catholic faith, it could push away voters.
Corroon's campaign tried to do just that Friday. Lieutenant governor hopeful Sheryl Allen, a Mormon, accused the LDS governor of trying to interject a "religious wedge issue" into the education debate by mentioning seminary.
"I'm a little surprised," Lyons said, "that with a substantial lead in the polls that [Herbert] would take his campaign in that direction."
Herbert remains far ahead of his Democratic challenger, based on the latest polls. Rasmussen Reports, a national purveyor of public-opinion data, conducted a telephone survey of 500 likely voters Monday and found the governor up 60 percent to 29 percent over Corroon. The poll had a 4.5 percent margin of error.
Then again, religion might not pose the biggest problem for Corroon. More damage could come from perceptions of elitism.
"What a private school says is, 'He's not like you,' " Monson said. "Campaigns are won and lost on how well a candidate resonates with the average voter. Are you seen as being one of us?"
The private-school debate has pried a little too close to home for Corroon, who called it "unconscionable" for Herbert to draw his family into the debate. He said his decision about where to send his daughter and two sons wasn't about the quality of the public school system. It was about Madeleine being his neighborhood school. It was about it aligning with his faith.
"It is just the right choice for us," Corroon said. "It doesn't mean that we don't have a good public school system."
The Herbert campaign insists the governor's statements against Corroon were meant only to question his credibility for critiquing public schools. It was not an attack on Corroon's children. It was not an attack on his personal life.
"The governor feels that Peter Corroon can educate his children anywhere he feels is best," Olsen said. "If you don't choose to be a part of it, then don't set yourself up to be a critic of it."
Kim Burningham, a member of the Utah Board of Education, said parenting a child in the public school system is "an important bit of training" for any governor.
"I would prefer [a governor] had some experience with the public schools so they can speak from that perspective," he said. However, "I don't think it is an impossible barrier."
Corroon sees his running mate as perfect for the public-education perspective. Rep. Allen, R-Bountiful, is a career public-school educator.
It wouldn't be unprecedented for a Utah governor to put his or her children in a private school. Gov. Jon Huntsman Jr., a Mormon, had at least one child enrolled at Judge Memorial Catholic High School during his tenure.
A week of charges and countercharges
• Democrat Peter Corroon unveils his plan to improve public education. The state must stiffen graduation requirements, cut corporate incentives that pull money from schools and put a higher priority on school funding.
• Republican Gov. Gary Herbert responds, saying that Corroon's comments are borderline "hypocritical" because Corroon sends his children to a private school.
• Corroon's camp fires back, accusing Herbert of a "personal attack on the Corroon children."
• Herbert criticizes Corroon's education plan during his monthly news conference on KUED as a "tax hike waiting to happen." He then suggests that the higher graduation requirements could eliminate LDS seminary courses.
• Corroon calls a dueling news conference, saying that his graduation proposal provides plenty of time for seminary. The Democrat says he hopes the governor isn't trying to play a "religion card" by first mentioning Corroon's decision to send his children to a Catholic school and then accusing him of threatening seminary.
• Sheryl Allen, running as Corroon's lieutenant governor candidate, later accuses the governor of using the Democrats' education plan as a "religious wedge issue."