> I have never understood why "reductio ad absurdum" is popularly considered a 'fallacy'.
> It seems like a perfectly logical argumentative technique,
It's both. The strong form of the valid argumentative technique involves what amount to a series of valid syllogisms, where each step from the premise to the false conclusion involves a true premise and a logical (and therefore absolute) implication. The false conclusion drawn through valid implication and and a series of premises all but one of which is accepted as true thereby disproves the premise that was in doubt. There is a weaker but still valid (though not in the logical sense) form, where the steps aren't logically necessary but contingently true, with both the intermediate premises and the inferences with high enough likelihood that the conclusion is very likely true if the questioned premise is true.
The fallacy has a similar shape but involves intermediate premises that are false or at least unjustified, or intermediate steps that are unwarranted, or consists of steps that are a likely enough individually but which in aggregate are not sufficiently likely to justify the conclusion that the premise is false.
Most commonly, the fallacy form rests on what reduces to the reasoning:
1. If A, it is most likely that B
2. Most likely A.
3. Therefore, most likely B.
A contradiction (A ^ ~A) is the point at which reductio ad absurdum is achieved. It proves that a false assumption was made.
A counter example to a universal proposition is but one means of finding a contradiction since the universal allows you to assert the positive. A proof that no examples exist would contradict the statement that some do, just as effectively achieving reductio ad absurdum.
What you're saying is not incongruous with what I'm saying.
statement leads to contradiction -> "general-statement is actually false in at least one case", so if reductio ad absurdum is defined as achieving a contradiction, then the original statement is false in at least one case.
It seems like a perfectly logical argumentative technique, designed to point out when a general-statement is actually false in at least one case.