Let me give you an example.

I've had people try to "debate" gay marriage.

I get "facts" by anti-gay organizations that spout bullshit. Now, I have two options.

I can counter with my own statistics and studies, but that's a losing strategy. Neither of us will accept each other's sources. There's no way we'll even be able to agree on the facts. (Consider Stanley Kurtz's argument that acceptance of gay relationships increased divorce: http://www.huffingtonpost.com/barrett-brown/stanley-kurtz-tr... is a refutation.)

I have my story. I have the stories of people in my position. However, if they're dismissed as irrelevant in favor of "logic," we have a problem.

Why? Logic depends on a few things:

1. A shared agreement on the facts.
2. A shared basis on axioms.

From there, the logical structure can be built upon the facts and axioms. However, if there is no agreement on the facts or axioms, what use is logic going to be? Certainly, it can be used to show internal inconsistency, but these arguments are often logically inconsistent.

For example, take the (very bad) argument:

1. Children with low IQ parents are more likely to have low IQ.
2. Black people statistically have lower IQs than white people.
(Hidden axiom: children with lower IQs are inferior to children with higher IQs)
Thus, interracial marriage is socially harmful.

Now, this is a logically consistent argument. However:
Premise 1 may or may not be flawed: People in poverty statistically have lower IQs, but this is not known to pass on to future generations. Poverty is a major confounding variable here, and there may be alternative explanations even if the premise is generally true.

Premise 2 is flawed. Many of the IQ studies are based on older tests, for example, and do not take poverty or education level into account. Older tests sometimes have cultural knowledge fundamentally embedded. However, it is paraded as a "fact" and has for a while, long before "The Bell Curve" came about.

The hidden axiom is also flawed, but this one is hairier and is a much longer conbversation. However, the conclusion depends on the exposure of this axiom. (Consider that what is true for the whole is not necessarily true for an individual case.) However, if there is no agreement on the axiom, the overall argument cannot be rationally discussed.

Thus, what is the logical basis of such an argument?

Further, can you imagine a black person being forced to try and have this discussion? He's implicitly being attacked by the argument itself. If he gets emotional, is that because he's not "logical" enough?
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Now look at an argument like racial profiling. There are two flawed premises that come up. First is that because there are more black people in jail, they are more likely committing crimes. (Consider that most studies have shown that an equal amount of white and black people smoke marijuana, but black people are significantly more likely to be arrested for it.) Second, and to the point here, is to deny that black people are disproportionately targeted.

The argument may be that white people are stopped on occasion too. However, the experience of my black friends and the experience that I have with the police are substantially different. If I went by my own (middle class white man) experiences, I would think that the police are generally helpful. This ends up being complete bullshit.

However, unless I talked with people who weren't white and middle class, I would have a fundamentally untrue assumption of the experience of others. If I value my own experience without questioning if I have blind spots, I am not checking my privilege.

The correct response to someone who argues out of this type of ignorance is to tell them that their experiences are not indicative of many others. There's no "debate" to be had because you will never even agree upon the axioms.

Why waste the emotional energy?