Many saints have scourged themselves, so we must take it that it's a wholesome practice, if undertaken the right spirit. However, in this post I'm not so much thinking about literal self-flagellation as rhetorical flagellation. Furthermore, I'm thinking not so much of self-flagellation aimed at oneself, as self-flagellation aimed at a group of which you are a member.
And, in fact, I'm not even going to make an argument in this post. I'm going to express an emotion. The emotion is distaste, and the context in which it arises is when a member of any group lambasts that group, regardless of how much that person may include himself in the condemnation.
C.S. Lewis's excellent essay "The Dangers of National Repentance" criticized young British people after World War Two who were eager for Britain to repent of its sins during the war. As he explains, they weren't really thinking of their own sins-- they were thinking of the sins of their elders, of jingoists, of patriots. Chastising Britain cost them nothing at all. Indeed, they took pleasure from it.
This is how I feel when I hear a male feminist, or a white person who is simmering in white guilt, or an American who never stops bashing America, or a Catholic who is denouncing the Catholic Church for its sexism, homophobia, etc. etc. Does it really hurt a liberal Catholic to bewail his Church's sins? Does he feel the lash on his own skin? I very much doubt it.
But even if he did, I would still find it icky. It's a noble and salutary thing for someone to to hold up his hands and say: "Sorry, that was my fault." But...isn't there something cringe-inducing about somebody who is always doing this? Don't you want to flee from someone who is perpetually apologizing? Don't their apologies feel strangely aggressive? Is grovelling ever anything other than odious? And don't the answers to all these questions apply to the group, as much as to the individual?