Of the many public apologies I've read in the past this reads like an honest, genuine one. He admitted guilt, explained what he did wrong and did not try to justify it, and clearly stated that he apologizes. What's missing?
Expression of regret. "I am truly sorry." - Check.
Explanation of what went wrong. "I must have directed angry words at you, who clearly had nothing to do with how the day had gone." - This is weaselly. "I must have...", not "I did".
Acknowledgment of responsibility. " I clearly forget that I am the oldest and most experienced—and I should act this way in a post-mortem conversation." - Weaselly. Whether he was oldest and most experienced or not, no one should behave this way. And rather than taking the responsibility, it's chalked up to forgetfulness.
Declaration of repentance. - Nothing here. No commitment to change. No stated intention for better emotional management.
Offer of repair. - "Finally, as you surely recall, I encouraged you throughout 2019, in person and in email, to join the Racket leadership;" In the absence of any kind of effort or commitment to change, this would not be received as a positive offer. But rather an extension of exposure to an abusive individual. Not much of a repair.
Request for forgiveness. - Nothing here either.
Well, I personally think asking for forgiveness is manipulative and shitty behavior. An apology should be about doing right by someone you wronged, not closing with "And last but not least: What's in it for me?!"
If they forgive you, coolios. Though it might take them more than five minutes just like it took apparently months for this apology to happen, so they don't need to promptly give you a fucking pat on the head like we give five year olds a cookie to reward desired behavior or some crap.
The capacity of such a request to be manipulative is dependent on first, the sincerity of the desire, and second, on the degree to which the injured party feels compelled to forgive. We do a disservice in the extent that we inculcate an expectation that a request for forgiveness must be granted, as coerced or compelled forgiveness is not meaningful as it does not represent a restoration of the relationship that was damaged.
I think it also depends on the severity of the offense. I think if someone murdered someone beloved by the person to whom they are apologizing or raped someone or ruined their career, it would also be gauche to impose and ask forgiveness.
Forgiveness is a gift. I don't think it is appropriate to demand a gift, especially if you have done someone egregious harm.
But I would suggest that rather than making the effort to hinder what may be a genuine attempt at the restoration of a relationship, we should instead seek to help people recognize that forgiveness is voluntary, and that they have every right to decline extending forgiveness if harmed.
To use your phrase, we need to make it a socially acceptable response to deny forgiveness.
Better that forgiveness be rare and sincere, than common and meaningless.
If they denied forgiveness in the first five minutes because they were hurt, many other people will reinforce their choice and actively make it difficult for them to sincerely change their mind.
At best, we can suggest that it should be socially acceptable to neither accept nor deny the apology and to not comment at all on the matter of forgiveness. But I think a public apology implicitly is a request for forgiveness and can be understood as such without a public request for forgiveness.
That's how I would handle it.
I used to write a lot of very sincere, public apologies on a small email list of a few hundred people because I was very ill and on a lot of medication and in a lot of pain and frequently not sleeping well. I certainly did not mean to offend anyone.
I wrote my apology. I explained what I had been trying to say if I felt it had been misinterpreted. I took responsibility for hurting them. I tried to write in a way that remedied that hurt.
The result was that I became the list scapegoat. If someone actively picked on me and I gave push back, then other people were all "There she goes again!"
I have probably more experience than average writing sincere and heartfelt public apologies. This is an informed opinion and it isn't going to change.
I always hated seeing on list apologies that ended with a request for forgiveness. They were consistently shitty behavior that boiled down to trying to save face and demand that the person they had wronged should make them feel okay about their sense of embarrassment. It was always an awful thing to witness.
Edited because autocorrect borked something.
But more importantly, he never admits to being a bully. The original post gives this incident as an example of a pattern of abusive behavior. He sidesteps that entirely.
It's also easier in some ways, because you can get help from experienced outsiders who have a stake in your success and you can afford to experiment with improvement methods without getting fired. There are ways in which it's harder, such as if employees are too scared to tell you when you're being nasty.
If someone hits you 100 times and issues you an apology for 1 of the times because somebody else saw him do it and thought it looked mean, does that absolve him of the other 99, which weren't mentioned in the apology?
Taking real responsibility for a pattern of abuse looks a lot different and will require some self-reflection and real steps toward justice.