Oi! Tons of ink (and blood) have been spilled over this one. I'll give it a quick shot. I'm by no means an expert, but I have done some reading, and may be able to apply a few facts to a discourse dominated, in my opinion, largely by "because I said so, and here (Colt .45 presented, barrel forward) is my proof."

The one constant is that a "son of God" is, in some way, divine. Note the "male-centeredness" of the Judeo-Christian-Islamic tradition; one never hears of a "daughter of God". In Genesis chapter 6, the "sons of God" are fully divine, a part of the "heavenly host". In some Judeo-Christian literature, "a" son of God is a mortal who expresses divine qualities - a saint, or a prophet. But in Christianity, "the" son of God is Jesus of Nazareth, a demigod (offspring of God and a mortal) with prophetic abilities, who rose from the dead after being judicially murdered, thus symbolizing the redemptive power of "God's love" on Earth. This resurrection is celebrated in the principal Christian festival, Easter - the name of which, ironically, is derived from a pagan (Celtic, I think) rite or divinity of springtime.

Demigods litter the Greek pantheon: Herakles (Hercules) was a demigod. The concept was previously unknown in Judaism (except for Genesis 6), and its application to Jesus of Nazareth is ironic, because his movement may have arisen from a sect of Judaism that throughly hated all things Greek (see 1 and 2 Maccabees). Elevation of Jesus to demigod status, though, would have appealed to the Greek Gentiles who made up most of the early believers in "The Way" after the Jesus sect ("Messianists") was thrown out of Judaism near the end of the first century CE. But Jesus was the only demigod in an otherwise monotheistic ("one God") tradition; this would have enhanced his divine status and redemptive significance for believers.

Enhanced it to the point that, to a Christian, anyone who denies demigod status to Jesus of Nazareth is someone to be fought - "love your neighbor" be damned. Jews, of course, denied this from the first. Muhammad, in the Qur'an, expressly denied Jesus's "divine sonship", correctly perceiving that a religion that professes to have "one God" can't have two. He praised Jesus to the skies as being one of the great prophets of God. But, obviously, to Christians, that ain't good enough. See "blood", above. And, of course, when the Scholar's Version of the New Testament translates words applying to Jesus, and in most Bibles appearing as "The Son of God", as "a son of god" (which, I gather, is closer to the original meaning of the Greek), all hell breaks loose.

So, back to the beginning. The phrase "son of God" applies to someone who has divine qualities. That seems pretty simple. But naturally, the devil is in the details.

Hope this helps.

a "mono"theistic religion with two deities.

That contradiction runs throughout Judaism, since its sacred book (the Bible's Old Testament) was compiled over a millenium of Hebrew history and smudges over many variations in what the Hebrews/Jews believed. If Jahweh is "the one God", what's this stuff about angels / heavenly messengers? Or Satan, originally one of those angels? Or any of the "heavenly host" (including those "sons of God" in Genesis 6)? Judaism and its children differ from other religions of its time and later not so much by monotheism per se as by:

(a) the conceptualization of one divine being as superior to all others (which may have had something to do with the first appearance of empires, with supreme rulers, in human societies);

(b) the concern of that "supreme being" with ethical conduct among humans, modeling same and insisting on emulation (previous pantheons had, essentially, modelled humans rather than modelling for humans, which meant, by and large, they sinned as they damned well pleased);

(c) the recording of "sacred history" in book form, to attest to the existence of the Divinity and his [sic] concerns for, and commands to, humanity.

As for the Christian "two deities" problem, that was neatly (well, maybe not so neatly - tons of ink and blood here too) resolved by the concept of the Trinity - Father, Son and Holy Spirit. Which, basically, encapsulates the God, the Demigod, and the Divine Spark in Human Hearts (or "spirit"; another Greek concept) within one Being.

why don't they acknowledge or reconcile such contradictions?

If Christians were any good at acknowledging or reconciling contradictions within their faith, there would indeed be one Catholic church (catholic meaning "universal", "all-encompassing", not "sectarian" as most people now, reasonably, understand it) instead of (Roman) Catholic, Orthodox, and Protestant churches, and 1758 denominations within each one, all probably founded by one charismatic Authority whose pronouncements evoked reverence and loyalty in (usually) his hearers, regardless of facts (which, before the invention of the printing press and subsequent development of more or less universal literacy, were hundreds of times harder to come by than today). The early history of Mormonism, with its schisms and controversies, may well reflect what went on in the history of older faiths, how, and why.

I've been asking the same questions for years.

Save a horse, ride a cowboy!!!