I'd be proud if one of my children had the foresight to go to the Principal about a complaint they had. It shows intelligence, strength of will, and an appropriate and effective way to word a complaint. It sounds like a very mature thing to do.
It's the little brats who swear, goad, disrespect rules and boundaries that are the problem. You bet your bottom dollar their parents never said NO to them or sent them to their room. Personally, I think discipline should be kept primarily to the responsibility of the parents but I do think that given teaching staff have a role of care giver for 6+ hours a day, 5 days a week, boundaries should be established and robustly enforced.
The problem with the OP is that they approached the establishing of boundaries in entirely the wrong way. It's when boundaries are breached that you have to be firm and frosty, not before. Otherwise they'll take the mentality of "may as well be hung for a sheep as a lamb", which basically means if we are going to be treated like dirt, there may as well be a reason for it. The OP didn't afford the decencies that they probably would if speaking to a group of adults, so how the heck can they expect pupils to act maturely if they feel targeted from the beginning?
Schools are supposed to make the child ready for working life and employable. Would a business employ someone who spoke to people in a professional setting the way the OP does? I certainly wouldn't. Leadership is about setting a firm but respectful tone, not a standoffish "come on, challenge me, I dare you" tone.
I had a teacher at primary school who used to speak to us firmly but respectfully. He treated us as an adult workforce effectively, he gave us respect but expected it in return and guess what, he got it. Much more so than the shouty, bitter, grudgeholding teachers who seemed to constantly find their time spent more on conflict than actually educating and undetaking a lesson in the specified subject.
And on second thoughts, I'd actually feel a bit creeped out if back when I was a child, a teacher had said "follow my instructions, don't question them"...I'd feel trapped and as though I wouldn't be able to speak up if I felt something was wrong.
I am calling in to question if the OP is in the right mindset to be a teacher. They sound very immature (e.g. holding grudges from previous students from the previous term, 6 weeks ago), and on some sort of video-game inspired power trip. The primary objective of being a teacher is to educate. It's to allow and encourage pupils to open their minds, to discover, to be creative and to flourish. The OP seems more concerned with her personal feelings about some hurty words from earlier in the year. The standard of teaching and the standard of parenting has fallen drastically over recent years. No one has any respect or accountability any more.
Some children are out of control and that's a result of the parent failing to ensure discipline and also probably a product of the garbage agendas the school pushes on to them and the inadequacy of new recruit staff who are of a similar ilk generation where they only care about what the job can bring for them, not what they can bring for their job. Laziness often comes in to it as well. Our ancestors would be horrified at how society has fallen. Even standards of attire has fallen. When I was at school in the 2000s, the staff used to make an effort to be smart, pin striped skirts, blazer and tie for the males, some of the females wore woollen jumpers but these were usually matched with smart trousers. And when I worked at a school, standards were lower but still there. I see videos of staff with tattoos etc on show, dyed pink or green hair. How the heck is that setting an example of what's acceptable in the work place? People are joining the teaching profession for all of the wrong reasons and no doubt being allowed in to fulfil a box ticking quota.