No matter how you interpret that scene, someone fucked up on the guard's side. Either the one soldier overreacted, or the rest of Henry's guard froze up besides one guy. Doesn't matter, the end result was that the threat was not neutralized and the VIP was further endangered due to needing to defend the guard. Henry's first response should not have been to praise him, because unless he's now rewarding loyalty over competence this soldier pulled a Leeroy Jenkins.
This part I disagree with entirely. Shade didn't write in the other guards, but that doesn't mean they weren't there. Anne was removed from Henry's shoulders by Henry (He fought off the attacker!), and the first guard arrived at that moment. I assume the other guards didn't need to tackle the girl, and thus were around and prepared. Henry went on to stop the 'fight' and the guard even knelt down iirc, and they shared a few words. At this point the girl tossed a fireball at the guard's head.
The guard successfully removed the threat, was told to stand down, did stand down,
then got a fireball tossed his way.
Problem is, Henry used a false dichotomy to teach this lesson instead of explaining things to her like an adult. Anne had more choices than burning + execution of entire family or total forgiveness. Fines, demotion, temporary suspension, a return punch in the face, on the extreme end fire him. If she ever actually thinks about the words he was saying instead of letting Henry shock and awe her into submission with EDGE, Henry's argument and the lesson after about responsibility will fall apart.
Anne will never truly mature if Henry doesn't treat her like an adult.
Not sure how I really feel about this. Although it was a false dichotomy, that's only because the highest ranking person was
Henry, any other noble and the dichotomy wouldn't have been false. I personally think he was teaching a lesson. She asked for the man to be punished, and any other noble would have executed the guard if Anne were to be seen as any level of noble rank, and not punished at all if she were just seen as a commoner. If she asked for him
not to be executed, it would still have been an embarrassment to the noble and the man would just be 'removed' later. The other side is what I've already said, punishing the guard for doing his job is
bad. Morale drops, Henry is less likely to be trusted and less liked by his men, etc.
Of course, the reality is it
is Henry, so a simple slap on the wrist type punishment is doable, but again, it's bad to punish someone for doing their job. (there are a lot of variables to this. Nobles don't act this way, but if it was Henry's sister, and the guard didn't recognize her, and she acted that way, then the situation would likely be different. Henry isn't perfect after all and is very protective of his family.)
I also disagree with the statement that Anne can't grow to be an adult if Henry doesn't treat her like one. He isn't hiding the world from her or anything, though this does show he mitigated her impulsiveness. Any other noble would have likely let her burn the guard alive, via the fireball from before, without calling on a medic. Commoners are cheap after all. It's likely that everyone else she interacts with expects her to be an adult and treats her as such. I wouldn't be surprised if she's already gotten a couple of servants killed and it's now dawning on her, unless she's a complete secret, which I doubt since she's been taught at the castle for a year.
Instead he uses the threat of executing the guard as the only option beat down Anne's justifiable complaints as he cannot logically argue them successfully. Much like how
@MinorGryph said, if Henry is unwilling to make the crime and punishment public then a whole other range of options are available. Its just the fact the Henry refuses to punish one of his 'Toy soldiers' is what is holding him back.
Whether it's a lesson to Anne or not, there's no need to punish the soldier for doing what he's supposed to do. If it's a lesson for Anne, then 'shock value false dichotomy extreme edgy lesson ahoy!'. If it's not a lesson then 'manipulation because she's a stubborn teen that won't let this go'. Seriously, you can be the first lady's childhood friend and tickle her causing her to scream, but you shouldn't blame the blacksuits for hitting you with a taser if it appears to be an 'attack'.
I guess to address these points directly; the guard did his job. Anne's complaints aren't justifiable because the guard was doing his job. Henry cannot logically argue them because they're silly 'Mr. blacksuit did his job and I got hurt for 'attacking' the prince-consort. blacksuit needs to be punished!'. Also, Anne is a stubborn teenager (though it's been a year, so maybe not anymore, but it's what I'll assume for now) meaning 'he shouldn't be punished because he was doing his job' will be met with more 'but he broke my nose!'. If Anne is a secret, then it's even worse to have the guard punished for doing his job and hurting a 'commoner'. Henry refuses to punish a man that did his job correctly, this has nothing to do with not punishing his 'toy soldiers' as he
has punished them before, the thing with putting women at the end of the list.
Originally I wasn't going to add this, but I'm late to continue the discussion anyway so: This reminds me of when I was being taught gun safety. 'The gun is
always loaded. Guns are weapons, they can and
will kill.' It gets the point across a lot better than 'eh, you didn't load the gun so it's probably empty, besides, even if it goes off you'll probably miss anyway'.