It starts out with Celestia disingenuously describing yawning boredom as "a little less exciting, perhaps". Then her inner monologue says it eternally gives her "great pride" to open the ceremony. Even though in S1, she described a very similar ceremony as "always terrible" and was glad that the mane six destroyed it. This comic version of Celestia just feels... saccharine... while at the same time being rather two-faced. The TV version of Celestia seems more genuinely nice, while at the same time being completely open and honest.
Celestia welcomes an overbearing and insulting woman, and she's shown to have difficulty keeping a false smile on her face. After the woman leaves, one of Celestia's more-experienced teachers makes a tension-breaking remark about the woman's marital relationship, and Celestia chides her underling for speaking out of turn. But what she actually says in her attitude-correction is that the woman has political importance? Not "don't be cruel" or "don't talk behind people's backs" or "her family relationships are none of your business"... Celestia's disciplinary response to an unwelcome joke is "I tolerate her because I have to"?
Then the rookie teacher says she's glad that she doesn't have to deal with this nonsensical political minefield of Celestia's apparent making, since she'll be working over at the kiddy table, and the experienced teacher jokes that kids can be an even bigger terror than politics. But don't worry, Celestia has total confidence that the rookie can handle the kiddy table just fine...
Then Celestia wants to know where Inkwell is, and the experienced teacher tells her, as if it's been obvious to everyone except Celestia for a long time, that kids are making fun of her. It seems that the only kids in the school who are willing to listen to Inkwell are the mean-spirited ones who are making a game out of observing how far Inkwell can fall into madness. Celestia shoots the kids a dirty look.
While socializing at the party, the experienced teacher is overheard expressing her frustration with Inkwell, and Celestia shoots the teacher another dirty look? Apparently Celestia's incompetent friends are an off-limits subject for party gossip. Celestia counters this insult by inviting her old friend to dine at the Princess' table.
Celestia also apparently invited the tiresome PTA leader to her table, and is going out of her way to make everyone miserable by dragging unwilling conversation out of her, instead of trying to cheer up her miserable, downtrodden husband, who is seated right next to Celestia, and seems to be happy for the opportunity for friendly conversation with anyone, even senile old people.
Then it seems that Celestia is somehow lacking in ability to quickly stop what basically amounts to a major food fight at the kids table, so Inkwell takes it upon herself to create a horrific monster that gets the job done, but traumatizes the children. "Your daughter was never in any real danger, she's just lying catatonic under a table, shivering." "I'm taking my kids home until I can be confident about this school's safety!" "I'm not going to let some know-it-all parents dictate my school's safety policies!" And then Emo Celestia needs some time alone to cry and convince herself that she's right.
"Every teacher wants to retire, but forcing her before she's ready would break her heart."
I don't think that's true. There are elderly people out there who refuse to believe that they've lost a step. Driving a car is a good example. If people don't keep an eye on their aging loved ones and draw attention to the signs of diminished capacity, many people will just get closer and closer to a very rude awakening. "Breaking their heart" is better than letting them kill someone, but an even better solution is to shine some light on the little mistakes, to make sure they don't just go into denial about them. Inkwell, I would say, is in denial. She's no longer effectively teaching anyone, and she seems to believe she's living on the frontlines of a warzone. She has obviously earned a place of distinction, and can involve herself with the school if she wants, but her role at the school is obviously not what it once was, and should officially be changed.
The resolution of the story, I wasn't too fond of either. Celestia gives Inkwell a very deliberately-chosen test, and Inkwell refuses to take the bait. Then Celestia gets way too ham-fisted in everybody's individual faces over "see see, did you get that point I was trying to make?" And then she puts on this false air of "Oh, but I follow my own laws, and Inkwell failed my test, so she's done for" and makes the parents beg for permission to have Inkwell continue traumatizing their kids. What would Celestia have done if the parents didn't beg? Or if Inkwell had turned the frog into another monster? That would've been rich.