One of the main problems I notice when I'm reading a debate or arguing with an "alternative" medicine proponent or religious believer is what we consider convincing evidence. We can both present cases filled with what each of us think is rock-solid, how-can-you-not-come-to-my-side evidence that is tossed aside as though it were meaningless. Why is that and who has the more solid ground to stand upon?
I think you know where my answer lies, but let's examine the question for inquiry's sake.
Oftentimes I will engage in conversation with, say, a believer in acupuncture. The most common point cited, in my experience, is that it is old. Thousands of years old. Something that has been around for that long has to be right because if it was not, it would have fallen apart by now. Nevermind that it's not thousands of years old at all and has no basis in reality - didn't you hear me? THOUSANDS!
Yeah, yeah, we are all saying the same thing in our heads: "argument from antiquity". The thing is, most people, believers especially, don't give two figs about logical fallacies; they care about what sounds correct from a "common sense" viewpoint. It's the old illusion that cave fish "lose" their eyes because they don't need them. It's totally wrong and the real answer is so much cooler and more interesting, but to many the first wrong explanation is stuck in their heads. Acupuncture works because it's old and it seemingly helps many people. End of story.
Not really. The trouble when having a discussion is that getting all sciency and technical seems pedantic. Belaboring a point that just feels right is like picking on something like Mother Theresa - "why do it, man? What do you have against helping people?" We have to pick both our words and our arguments carefully to avoid being seen as the condescending, science-worshiping a-hole.
It really is something to behold. I have been in the position before of (too often) citing Nobel laureates and had a comment thrown back at me that sounded a lot like: "Well look at this - oh, but it didn't come from a Nobel prize winner...nevermind." Sarcasm dripped like cold honey on that March day, my friends.
Also, the tactic of switching points is something to watch out for when you attempt to corner an alt. med. believer. In my experience, it usually happens when some "evidence" is presented - say, a study from a journal or a "fact" from the internet - and it is examined and you reply with specific questions. Think about an anti-vaxxer stating that there is antifreeze in the MMR vaccine. You point out that, no, there isn't and explain the difference between the chemicals concerned. Once that happens, you'll often see movement from discussing specifics to generalities about "toxins". I find that all this is is the believer turning away so they don't have to say that their mind has been changed. The next person they argue with will hear the same memorized point and Believer will just hope they can get away with it this time.
There are Creationists that have made careers out of that tactic. Ahem *cough-GISH-cough*
The main difference I note is the use and acceptance of anecdotes as valid evidence. Whether it's acupuncture, chiropractic, reiki, reflexology, or ear-candling, patients/clients say they feel better, therefore it works. End of discussion.
We as skeptics, science nerds, and critical thinkers can not leave it at that and we seem like Spocks for discounting people's experiences. Personally, I always make it a point to talk about Feynman's two things that people think that make any discussion between the skeptic and believer camps difficult: 1. People are very easy to fool. 2. No one thinks they're easy to fool.
Once this is established (ideally with some sort of cool sleight-of-hand trick), the argument, debate, discussion, or fight can jump off with some common ground.