Facebook has faced a fair amount of heat over its tolerance of Holocaust denial groups on the social networking site, especially from billionaire Mark Cuban’s attorney brother, Brian Cuban.

Yesterday, in an open letter to Facebook CEO Mark Zuckerberg*, Cuban reiterated his request that Facebook remove Holocaust denial groups. Cuban claimed allowing them to remain only helps them “spread their message of fear and hate.”

Facebook’s official response defended the hate groups’ presences on the site by defending its own policy of tolerance of open discussion. Facebook pledged to remove the groups if the open discussion turned violent.

Cuban was unimpressed with the response and put spokesperson Barry Schnitt (formerly with Google) on the hot seat in his open letter, noting that private enterprises are not bound by freedom of speech laws and demanding Schnitt and Zuckerberg reveal more about the decision making process involving the groups.

“By allowing these groups whether they number 1 or 1000, Facebook is not promoting open discussion of a controversial issue,” wrote Cuban. “It is promoting and encouraging hatred towards ethnic and religious groups, nothing more.”

Since Cuban’s letter, Facebook has been carefully monitoring five groups in question, waiting for members to advocate violence. Two groups have been deleted, leaving three. Cuban again went after Schnitt, calling him “disturbingly dismissive and flippant about these issues.”

Schnitt responded on CNet with a fair amount eloquence:

“Many of us at Facebook have direct personal connection to the Holocaust, through parents who were forced to flee Europe or relatives who could not escape. We believe in Facebook’s mission that giving people tools to make the world more open is a better way to combat ignorance or deception than censorship, though we recognize that others — including those at the company, disagree. We may be fools for doing the former but not ‘cowards’."

The battles Facebook chooses are interesting. The social network once also stood firm on its deletion of photos of breastfeeding infants. It’s a bizarre message—and a PR nightmare!—that Facebook is protecting the rights of hate groups while declaring nursing babies obscene.

Some touchy waters they’ve waded into, eh?

*Zuckerberg is a German Jewish name.