They were created after their kind and they procreate after their kind. That's what makes a kind a kind--procreation is constrained within the kind. Your wild speculation is unfounded.
Besides, we have no clue what method might have been used to produce any potential hybrid offspring. For all we know, it may not have been physical reproduction at all.
You've been indulging in too much science fiction.
Angels in heaven don't marry...
You suggest that angels who are cast out of heaven can break, as it were , their vow of chastity and start procreating. First, all angels and Satan are still in heaven. They have not been cast out heaven yet. That doesn't happen until Revelation 12:9 which coincides with the start of the persecution (tribulation) of the saints. Consequently, any theories involving post-heaven angelic beings procreating with men are non starters, because they are still in heaven. Second, after they are cast out, they will endure for only a short while until they are bound in hell or cast into the lake of fire (Revelation 19:20, Matthew 25:41).
The passage from Matthew 22:24-30 is specifically talking about "raising up seed" and states that angels do not raise up seed. Resurrected believers do not procreate because they will be like the angels of God when they (the resurrected believer) are in heaven. Fallen angels do not die like humans do and have an opportunity to be saved and resurrect. Fallen angels will spend eternity in the lake of fire which was made specifically for satan and his angels.(Matthew 25:41)
The Sons of God mated with the daughters of men and produced "mighty men of old, men of renown." It doesn't say they were giants. And if it had, it simply means they were very large men, not some new creature, for creation has ceased. God rested after day 6.
“They were created after their kind and they procreate after their kind. That’s what makes a kind a kind—procreation is constrained within the kind. Your wild speculation is unfounded.”
What wild speculation? The text says nothing about procreation being constrained, does it? Surely you can provide a citation for that, if it isn’t just your own “wild speculation”.
Also, while you are at it, see if you can find a verse mentioning these kinds and constraints in relation to men, or angels, since they are the ones seemingly involved in the potential union. Whatever animals or plants may be constrained to do doesn’t have a direct bearing on the question.
“You’ve been indulging in too much science fiction.”
If you automatically deem a non-physical, non-carnal act of reproduction “science fiction”, then I’m afraid you’ll have some issues with a major plot point in the New Testament.
“You suggest that angels who are cast out of heaven can break, as it were , their vow of chastity and start procreating.”
I suggest we don’t know whether or not, from the text, whether this is a prohibition intrinsic to their nature, or a command. If it’s intrinsic, then you could argue that there is no way they could. If it’s a commandment, then obviously disobedient angels might be able to disobey it.
“First, all angels and Satan are still in heaven. They have not been cast out heaven yet. That doesn’t happen until Revelation 12:9 which coincides with the start of the persecution (tribulation) of the saints.”
That’s one possible interpretation of things, but as it is a prophetic text, it can represent a future event, recount a past event, or even represent a long compound narrative stretching from the past to the future. There are all types of those prophecies in the Bible.
To me, it seems the final expulsion of Satan in that prophecy corresponds to the events of Revelation 9, with Satan as the star that falls from heaven with the key to the bottomless pit. If that is the case, it pinpoints his descent to Earth in the larger timeline of the tribulation, but it also reveals there are some demons or spirits who seem to have previously fallen from grace before Satan’s final rebellion. After all, they are already imprisoned in the bottomless pit when Satan arrives to free them.
Also, note that in Revelation 12:4, it says Satan drew down 1/3 of the stars, or angels from heaven, prior to the birth of Christ. The prophecy seems to describe two separate events, an initial rebellion, or fall of Satan and one third of the angels, and a subsequent war in heaven, at the end of which Satan and the angels are permanently banished to Earth. There are certainly plenty of other passages in the Bible supporting the fact that Satan and demons are free to walk the Earth at this time, and no solid indication that this wasn’t already the case in the time of Genesis.
“The passage from Matthew 22:24-30 is specifically talking about “raising up seed” and states that angels do not raise up seed.”
No, that is incorrect. The passage speaks of raising seed, because it was part of the Old Testament law that is being referenced by the Sadducees. It was the duty of brothers to marry such widows in order to give them children, and the Sadducees used that peculiar scenario, taken to the point of absurdity with seven brothers, to try and “stump” Jesus about the law and resurrection.
The key question is who the wife will “belong” to in heaven, since she had married all seven brothers, according to God’s law. Jesus cut the Gordian knot by revealing that, just like the angels in heaven, we will not marry. He never states that angels do not “raise seed”, or that they do “raise seed” for that matter.
“The Sons of God mated with the daughters of men and produced “mighty men of old, men of renown.” It doesn’t say they were giants.”
It calls them “nephilim” in the Hebrew. This is the same term used to describe the giant inhabitants of Canaan by the scouts in Numbers 13:33. It’s also used in that manner in quite a few apocryphal works, such as Enoch and Jubilees, which specifically tell of angels creating giants. The interpretation of nephilim as meaning giant, and the Sons of God being angels is the ancient, traditional interpretation of these verses, and not some innovation or personal speculation.
“And if it had, it simply means they were very large men, not some new creature, for creation has ceased. God rested after day 6.”
Well, yes, giants are very large men, but according to the Bible, at least when we read the descriptions of the post-flood giants, they are larger than any we see produced through normal human reproduction. As for it being a new creature or not, it seems a moot point, since they are in the Bible, described as existing, one way or another. You can’t wish them away by inventing rules precluding their existence.