Nihilism is a philosophical position which, to my college-uneducated self, is usually defined as: Social structures, values, or beliefs are unfounded, or that life or existence has no purpose or is senseless.

I’m not dealing with this in the philosophical sense, but in the manner Christian and Muslim apologists for their faiths represent it.

The usual claim is "atheists are nihilists, because they see no essential purpose to (life, the universe, and everything)." The assumption is that atheists are therefore only interested in their own selves and no one or nothing else (since values or ethics are antithetical to atheists, being nihilists).

It is another strawman of atheists.

Not believing in Kali-ma or any other goddess says nothing at all about whether an atheist values social structures or a society’s values, or believes there is no purpose to life. For example, my society values free speech to a high degree. It values equality of opportunity for all (though sometimes falls well short). It values the right to be secure in your person or papers. These and other values of society are considered important enough that they are written into my nation’s constitution. It takes no belief in a god to uphold those values (or indeed in my case, affirm under an oath that carries a penalty under law to uphold and defend them).

In XIX Century Dixie, slavery was part of the social structure: It was written in the law and in the US Constitution. Opposition to this position of the law and society did not make an abolitionist a nihilist. One could be opposed to that aspect of the antebellum USA and still support the rest of the country’s society and laws.

For that matter, even if one is completely opposed to everything the society stands for or writes into law does not make one a nihilist (for example, being opposed to a dictatorship and participating in a partisan force to overthrow it).

A nihilist sees no value in any social structures. If I was a nihilist in this fictitious dictatorship, joining a partisan organisation to try to overthrow it would be also pointless. If there is no meaning or purpose to life, why try to improve it for anyone at all?

As for the issue of a "point" or "purpose" to life, the universe, and everything (hat tip to Douglas Adams), one has not been demonstrated by any sort of science. That does not mean people cannot ascribe a point or purpose to life themselves (we don’t need a god for that). All sorts of "purposes" have been ascribed to life by all sorts of societies throughout history. Those points seem to vary by geographic and temporal displacement, almost as if the "point" of life is subjective.

The apologist, when applying the nihilist term to an atheist, is not using the term in a philosophical sense. He or she is conflating the term with "selfishness."

The assumption is that if I "believe" in evolution (as if it was a religion, rather than the best current explanation for the diversity of life on Earth based on multiple lines of evidence and testable theory), then life must have no "point." It is random and has no meaning (it is nihilistic), therefore I must be nihilistic (selfish).

This is the formal fallacy of Illicit Contraposition. (Borrowing a joke credited to John Congden, this is not a scandal from Ronald Reagan’s administration.)

The fallacy contends that anyone who is not a member of group X must necessarily be a member of group Y. (The fallacy ignores those in group Y who could hold the same positions as those in group X, or other positions not considered part of either group.) A simple political example might be: