"He's not a secular intellectual in the molds of Western intellectuals," said Baqer Moin, an Iranian commentator. "No, he's coming from within the revolution."
In fact he was part of the revolution, a supporter of the Ayatollah Khomeini when he came to power in 1979 - a government minister during the Revolution's turbulent early years.
"Then he became prime minister and was prime minister for nearly eight years," Moin said.
"Very much an establishment figure," asked CBS News correspondent Mark Phillips.
"Absolutely," Moin said.
Even if Mousavi came to power, the change he represents is more of tone than policy.
He may not deny the Holocaust, but he has made no promise to end Iran's support for the militants in Hezbollah or Hamas on Israel's borders.
And while he might be prepared to talk about it, he too is committed to Iran's nuclear program.
"He's a moderate, he's a pragmatist moderate," Moin said.
"In the Iranian context," Phillips said.
"In the Iranian context, absolutely," Moin said. "The Iranian system in not democracy nor a theocracy - it's a mixture of both."
The Iranian system, with the electorate at the bottom and the Supreme Leader, Ayatollah Khamenei, at the top - is a complicated, overlapping cocktail of religion and politics that no president could easily change - even if he wanted to.
Voters elect a 290-member parliament, a president and an Assembly of Experts, 86 "virtuous and learned" religious scholars who select the Supreme Leader.
But layered on top of this is a 12-man, extremely powerful, Guardian Council appointed largely by the Supreme Leader. It gets to decide who even runs for the presidency or parliament.
To that add an Expediency Council, appointed by the Supreme Leader, which is supposed to mediate disputes between parliament and the Guardian Council.
Whether they are demonstrating inside Iran or outside of it, supporters of Mousavi see him less as a counter revolutionary figure and more of a reformer. To them, he's become the acceptable face of the Iranian Revolution - one they're not ready to give up on yet.
This graphic shows the structure of the Iranian government.