A bunch of largely disconnected thoughts.
I agree with others here that if you're going to have this sort of debate, then your goal should not be primarily "convince my father to agree with me" but "improve the accuracy of both his thinking and mine", and talk of "arguments that I ... need help shutting down" is probably indicative of sloppy thinking.
If someone else has an argument that you can't find a good answer to, this doesn't necessarily mean that they are correct. It just means that you haven't found a good answer to that argument. There is nothing wrong with saying "Yes, that seems like a good point and I don't have a good answer to it right now, but it's not enough to convince me to switch sides." (But of course if you find a lot of such arguments on one side and way fewer on the other, it's suggestive of which side is nearer the truth.)
The parallel Keller draws between religion and science is badly broken. Specifically, if anyone said "Evolution just makes sense to me; I feel in my bones that it's right" and regarded that as a good reason to believe in evolution, then they would be terribly wrong, every bit as wrong as someone who says the same about God; but that isn't what anyone actually says. (Not anyone with a clue, anyway.) So, indeed, we can't trust our belief-forming faculties to deliver accurate beliefs about God or science or anything else merely by considering the question for a while and seeing what we find ourselves thinking; that's the whole point of the whole scientific apparatus of peer review and double-blind testing and quantifying everything and doing analyses with as-rigorous-as-possible mathematics and so on and so forth. Keller's argument would be a good response to someone claiming to know by intuition that evolution is correct and theism is wrong; or to someone claiming that purported rational arguments for God's existence are no good because our brains are fallible. But I don't think I've ever heard anyone take either position.
Atheists can be moral realists, but let's suppose for the sake of argument that you aren't one. Then the first place where your father's rape argument falls down badly (I think) is where he leaps from "it doesn't have an inherent wrongness" to "it was justified". A consistent moral nonrealist doesn't say "Everything is morally permissible" but "The whole idea that things are objectively permissible or not is misconceived". A typical moral-nonrealist position on rape or genocide or whatever would be something like this: "Strictly speaking, when you ask whether something is morally justified you need to say according to whose moral values. According to mine, [INSERT ATROCITY HERE] very definitely isn't morally justified, and reproductive success has nothing to do with moral justification. I'm sure the same is true of your values, and those of just about everyone else; it's a useful shorthand simply to say that it's morally unjustified, just as one says that sugar is sweet even though there are some people whose perceptions are weirdly different. Perhaps [NAME OF MONSTER GOES HERE]'s values were radically different, or perhaps he had none at all, but mine are much like yours in this respect, and I will fight alongside you against such atrocities. I just don't see any reason to think that those values are woven into the fabric of the universe. It suffices that they are woven into the fabric of my mind."
To expand slightly on one bit of that: There is absolutely no shred of a reason why someone who believes in evolution, or someone who doesn't believe in a god, or someone who is or isn't a moral realist or a moral relativist, should believe that moral justification has anything to do with reproductive success. (In particular, it no more follows from belief in evolution than it follows from belief in gravity that it's morally obligatory to move heavy objects closer to one another.) If someone tries to foist such an idea on you, you might ask them to explain exactly why.
It's worth being very clear about just what it is that he's asking for explanations of. For instance, it's clearly reasonable to ask why people make moral judgements, why they agree to the extent that they do, why they tend to feel like perceptions of universal truths, etc.; it's less reasonable to ask how we know that moral judgements are perceptions of universal truths, because that assumes something highly debatable.
It's OK not to have explanations for everything. More precisely, someone might demand an explanation for something (a) when it turns out to be true, despite good reasons to expect it to be false; or (b) when it turns out to be true, despite there not being an obvious reason why it should be. But these are very different situations. In case (b), if you don't have an explanation, all it means is that there's some stuff you still don't understand. Fair enough; there's lots that we don't understand. In case (a), if you don't have an explanation, then it means there's likely something actually wrong in your thinking, because those "good reasons" are leading you astray. It seems to me that, e.g., "why is the world full of things that according to Christian ethics are evil and unjust and bad, if there is a supremely powerful and good being who cares about our affairs?" is a type-A question, whereas "why do we make moral judgements that feel to us like perceptions of universal truths, if in fact there are no universal moral truths?" is a type-B question.
I think it's unlikely that reading Eliezer's writings on morality will help you much in these debates. (You might still find them interesting, of course.)
So, a little background- I've just come out as an atheist to my dad, a Christian pastor, who's convinced he can "fix" my thinking and is bombarding me with a number of flimsy arguments that I'm having trouble articulating a response to, and need help shutting down. The particular issue at the moment deals with non-theistic explanations for human psychology and things like love, morality, and beauty. After attempting to communicate explanations from evolutionary psychology, I was met with amused dismissal of the subject as "speculation".
There's one book in particular he's having me read- The Reason for God by Timothy Keller. In the book, he brings up evolutionary psychology as an alternative to theistic explanations, and immediately dismisses it as apparently self-defeating.
"Evolutionists say that if God makes sense to us, it is not because he is really there, it's only because that belief helped us survive and so we are hardwired for it. However, if we can't trust our belief-forming faculties to tell us the truth about God, why should we trust them to tell us the truth about anything, including evolutionary science? If our cognitive faculties only tell us what we need to survive, not what is true, why trust them about anything at all?" -Timothy Keller
The obvious answer is that knowing the truth about things is generally advantageous to survival- but it hardly addresses the underlying assertion- that without [incredibly specific collection of god-beliefs and assorted dogmas], human brains can't arrive at truth because they weren't designed for it. And of course, I'm talking to a guy with an especially exacting definition of "truth" (100% certainty about the territory)- I could use an LW post that succinctly discusses the role and definition of truth, there.
Another thing Dad likes to do is back me into a corner WRT morality and moral relativism- "Oh, but can you really believe that the act of rape doesn't have an inherent [wrongness]? Are you saying it was justified for [insert historical monster] to do [atrocity] because it would make him reproductively successful?" Armed only with evolutionary explanations for their behavior, I couldn't really respond- possibly my fault, since I haven't read the Morality sequence on account of I got stuck in the Quantum Physics ultrasequence, and knowing that reality is composed of complex amplitudes flowing between explicit configurations or aaasasdjgasjdga whatever the frig even (I CAN'T) has proven to be staggeringly unhelpful in this situation.
In addition to particular arguments WRT the question posed, I could also use recommendations for good, well-argued and accessible books on the subject of evolutionary psychology, with a focus on practical experimental results and application- the guy can't be given a book and not read it, so I'm hoping to at least get him to not dismiss the science as "speculation" or a joke. It's likely he's aware that the field evolutionary psychology is really prone to hindsight bias and thus ignores it completely, so along with the book, a good article or study demonstrating the accuracy and predictive power of the evolutionary psychological model would be appreciated.
Thanks!