The most common unproductive way to disagree is to attack your opponent, rather than what they have to say. (This is called “arguing ad hominem”—Latin for “against the person.”)
Ad hominem rarely adds to understanding—but it can be effective at silencing opposition.
Here are some specifically Buddhist forms of ad hominem I’ve encountered:
“You are being aggressive.” In other words, you won’t shut up when I tell you that you are wrong. “Aggression” is the worst Buddhist sin, so if I can make that stick, nice Buddhists will ignore whatever you have to say. (This also trades on the wrong idea that it is inherently hostile to insist that different Buddhisms are different.)
“Obviously, you don’t practice meditation much.” If you did, you would agree with me. Because meditation leads to the Truth, and I have the Truth.
“This is a bunch of academic/intellectual posturing.” I find what you are saying hard to understand. I don’t actually know much about Buddhism, but I’m totally sure I’m right. Rather than learning more—perhaps even from you—I will try to make you look irrelevant and out-of-touch.
“You have no right to say that.” As you know, we live in a totalitarian state in which The Buddhist Authorities determine who is allowed to say what.
“That’s not compatible with our Western values.” Naturally, all good Westerners have the same values, namely mine.
“That’s just a traditional view.” (The usual way for modernists to dismiss traditionalists.) As of last week, we’ve got everything figured out, so anything that contradicts our current belief is obsolete and should be forgotten.
“Your Buddhism is inauthentic.” (The usual way for traditionalists to dismiss modernists. What does “authentic” mean? In practice, nothing more than “my system, not yours.”)
“Yours is even worse.” You don’t believe that my meditation can make me One with The Entire Universe? Well, I don’t believe in your Tibetans’ flying lamas, either.
What other unhelpful Buddhist argument styles have you encountered?