I agree that respect should never be demanded; however, you have to admit there are people in this world that would never give anyone respect no matter how cool they were.
I was in the Navy for six years. Engineering is a very close-knit department, full of people who really are good friends. I also cranked up in the wardroom, and knew a lot of the officers really well.
But no matter how cool I was with officers, or even the CO, it would not be my place as an E-4 to walk into the Captain's Cabin and go, "Hey skip, what's up?" There are certain levels of familiarity that cannot, SHOULD not be given in situations of authority. Are teachers and students one of those situations? Well, no, not really. But still, first name basis and being able to goof off with a superior is a privilege, NOT a right, and I think that's part of the problem. People think it's their God-given right to be able to be close friends with superiors, and I'm sorry to say that's not true.
Even God, the greatest Superior there is, demands we respect Him. We can call Him Father, and we are close to Him, but He is still our God and Master, and we bow to Him, and we are His servants. See what I mean?
I'm the opposite of you, Hakaii, I would actually be very reluctant to be in a class with a teacher who asked us to call him by his first name and acted like our buddies. That would imply to me he doesn't take his job seriously. He's a professional, he should act like one, he should be addressed properly, and he should be approachable and friendly...but he is still a superior.
"its not MY job to re-teach things that your previous teachers have failed to teach you. you'll just have to go back and retake those subjects."
You know what? She's right. It ISN'T her job. If she's a calculus teacher, she shouldn't have to teach people basic algebra. They should already know it. If they don't, they shouldn't be in a calculus class. It's as simple as that. Now, I admit that for her to say it in a nasty tone and without any prompting, was probably a bit harsh. But she is completely right, that it is not her job to teach things the student should already know.
Now, is every student going to remember every single thing from previous classes? No, of course not, and a teacher should always be willing to give short refresher lessons, i.e. "Okay, you may not have messed with logarithms for a while, so in case you forgot..." But they should not be forced to reteach logarithms completely. That's what tutors are for. Trying to go over subjects that should already be known merely slow the rest of the class down, and slow down the lesson plan for the year.