I work with children, if one is rude to me I always tell them that I show them respect, I expect respect back, even if they don't like me. I also expect them to treat each other with respect. I never say the 'I'm a teacher so you should show me respect' line because I don't think that they should be taught that they MUST respect people who are older or in authority. Obviously when first meeting someone they should, but if that person doesn't show them respect then why should they? Respect should be mutual.
I don't like the 'respect your elders' thing. I know quite a few people born in the 50s/60s who were either physically or sexually abused but were too scared to speak out because they had to 'respect their elders' and were afraid they wouldn't be believed as they were just a child.
I also know quite a few older people who are downright rude towards younger (especially teenage) people are expect respect back. My own nan in particular thinks she can say/do as she likes and we should just accept it, including telling me to quit uni and work in a shop as that's all I'd be good for. When she's challenged on it she says 'i've earned the right to be able to say what she likes at my age' and is completely serious. She bullies my poor cousin who's too scared to stand up to her as my nans so nasty to her.
Some people just don't deserve others respect, no matter their age.