I’m reading GAE by @swamidass and recently got through the section on chapter 11 about Nephilim. I found this section particularly compelling for his argument. It’s a difficult passage and it’s hard to know what to do with it. He suggests it may have something to do with interbreeding and genetics. Well, basically everyone thinks it has something to do with hybrids and interbreeding. So I had to decide what do I think Genesis 6:4 means?
I was studying it more, and then it hit me - it has to interbreeding and genetics of course! 
What do I mean by that? IMO various interpretations are reading way too much into the text, and we should think about it from basic human experience AND also from a female’s perspective. I’m only reading men’s interpretations. Let me stick up for women here. I’ll explain as I go.
We like to look at our kids and notice where they got their physical features from - mom or dad. This has to do with genetics - but even people who had no knowledge of genetics centuries or millennia ago, would have easily noticed their kids had mom’s nose, or dad’s eyes, etc. I think Genesis 6:4 is a parenthetical reference just to give some extra information.
What else surrounds the Genesis 6:4 verse? There’s a discussion of sons of God seeing beautiful women and taking wives of all they chose. To me this verse is talking about powerful men lusting after beautiful women and being promiscuous, much like we see with David and Solomon.
@swamidass references Bodie Hodges from AIG in his book Nephilim: Who Were They? | Answers in Genesis
He mentions various views, in some of which the sons of God could be referring to rulers or some of Seth’s lineage. I agree with those two views.
But notice he’s assuming the daughters of “men” in comparison to the sons of God means the emphasis is that the women were ungodly. That’s possible, but I don’t think the text is emphasizing that as the most important detail here. What’s the important detail it seems everyone is leaving out? "And the Lord said, “My Spirit shall not strive with man forever, for he is indeed flesh; yet his days shall be one hundred and twenty years.” What I interpret this passage to be saying is that God is seeing that the longevity of man is adding to his sinfulness. Then the text adds some parenthetical references of another consequence of longevity and marrying beautiful women: giant men.
Bodie Hodges mentions:
"Interestingly, Moses, who penned Genesis, said that the Nephilim were on the earth pre-Flood and also afterwards:
Genesis 6:4a
The Nephilim were on the earth in those days— and also afterwards (emphasis added)
Some translations say “and after that,” and one could argue that this was still referring to a pre-Flood time. However, it makes much more sense that this phrase refers to this post-Flood event, especially since Genesis 6 was penned by Moses."
The passage to me is making a distinction that after the flood, Noah’s sons did not have this gigantic trait; instead it was a trait of one or more of their wives, perhaps a recessive trait.
I think that’s also the emphasis of Genesis 6:2 - that the women were particularly beautiful because they were tall. Models today have to be tall. Who else do we consider to be tall, exotic women? It popped in my head - the Amazon women. hmm… The Amazon Women: Is There Any Truth Behind the Myth? | History| Smithsonian Magazine
I checked out more passages on gigantic men in the Bible to confirm my exegesis and was going to type those out, but then I realized AIG had an excellent article here: Giants in the Bible | Answers in Genesis
The author there even discusses legends around gigantic men…but leaves out the gigantic women 
I agree the text, at first, doesn’t initially emphasize tall women, but you can probably see if you look at it the way I am - that the “Sons of God” line were strong, muscular men, and the daughters of men were beautiful tall women, they would produce beautiful, strong, muscular, tall men. Always emphasizing the men… 
This is relevant to me because I am a very tall woman - 6’0". My husband is tall. My two boys are giants. They have been in the 95-99 percentile. My son just turned 4 and weighs 54 pounds. I assume that we have more Neanderthal DNA than most - they were tall and European correct? I’m also ethnically Dutch, considered the tallest people in the world. But I think that may actually be prejudiced and too focused on Europe. https://www.youtube.com/watch?v=u03kNQNclGY
Notice that in the Smithsonian magazine article, it describes the ancient Greeks decided the Amazonian women must be Scyhthians. That would put them in Japtheh’s mostly European lineage, maybe relating them to Neanderthals, and me too! 
I was just think that height might be a fascinating genetic study, especially since the Bible emphasizes which people groups had this height gene, even clarifying they were called by different names by different groups.
“The Emim had dwelt there in times past, a people as great and numerous and tall as the Anakim. They were also regarded as giants [Hebrew rephaim ], like the Anakim, but the Moabites call them Emim” (Deuteronomy 2:10–11).
It seems there are already some studies Scientists Discover the Genes that Decide How Tall You Are | TIME
I would love to know if I’m related to the tall people of South Sudan. Sign me up for that genetic testing and comparison 
That sentence has to be talking about men only I think. 
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