One of my instructors just gave my classmates and I a bit of a "motivational speech". One of the things she said got me thinking, and I'd like to know what you all think.

I will use quotes, but I'm not sure it's verbatim.
"For anyone to respect your opinion, you must stick by it even if it's wrong."

I'm sorry, but I you know you're wrong, how is it respectable to ignore what is right? Opinions?

She is arguing an extreme IMO.
People cannot respect a statement you made, if you can't stick with that statement. What it seems she failed to mention, is that you need to pick your battles.

On a somewhat related note I often enter a debate, supporting a side that I don't agree with. To win this debate, or even stand a chance, will take great conversing skills, and you will also learn to understand, or even respect, that side of things. Making you a wiser person.

I don't think she is trying to tell you to ignore what is right but more like "don't just give up on your side of a debate if you or the majority of your peers think it's wrong because it makes it almost impossible to respect your side of the argument." now if you get beat fare and square in a debate there isn't anything to do about it. But if you are in a debate that doesn't have one specific answer, then confidence played a major role in how persuasive you can be. For instance, there was a debate in one of my classes a few weeks back about legalizing marijuana in the U.S. and i was assigned to the team arguing that if it was legalized, it would decrease crime and drug abuse. I personally believe that legalizing marijuana is a horrible idea but that's beside the point. I had all odds against me because my team was a bunch of slackers, the teacher rarely let the side she didn't believe in win, and everyone else in my class was siding with the side saying don't legalize marijuana. Instead of saying "screw this, I know this is wrong so i'm just not going to do anything" I stuck with it, found some actual evidence, and attacked it head on. It ends up I won the debate for my team because everyone recognized my facts where rock solid, and I stood up believing with all my soul that I could win that debate. The moral of my story is if you are given a topic to debate that you don't believe in, no one will take you seriously if you don't take your topic seriously and attack it with everything you have.