I do laugh at myself at times. But for this time, we're talking about a serious matter. I'm not laughing.
You obviously don't understand what Paul was saying there in Hebrews 6.
How is it you skipped the 2 previous verses that go with that one Hebrews 6:6 verse? Who am I to show you 'how' to study God's Word at your ripe age? You should well know how by now.
Heb 6:4-9
4 For it is impossible for those who were once enlightened, and have tasted of the heavenly gift, and were made partakers of the Holy Ghost,
5 And have tasted the good word of God, and the powers of the world to come,
Those 2 verses reveal this is about a believer with a definite chosen calling by God, one of His chosen elect servants, not a new babe in Christ, nor just a believer that has a hard time with sin yet still believes on Christ. This appies to someone which God has worked miracles through even, and that person knows it, with no doubts. That's the condition for understanding the next verse...
6 If they shall fall away, to renew them again unto repentance; seeing they crucify to themselves the Son of God afresh, and put Him to an open shame.
This is not about little slip ups in small sins all believers may commit after having coming to Christ, and need to repent for. This is about one of His chosen elect turning completely away from Him to follow the world instead. And this world today belongs to the devil (Luke 4). Paul is going to stress that point in the next verses too...
7 For the earth which drinketh in the rain that cometh oft upon it, and bringeth forth herbs meet for them by whom it is dressed, receiveth blessing from God:
8 But that which beareth thorns and briers is rejected, and is nigh unto cursing; whose end is to be burned.
9 But, beloved, we are persuaded better things of you, and things that accompany salvation, though we thus speak.
(KJV)
If you feel this Heb.6 matter applies to yourself (I already know it doesn't), then it would mean you should as a result expect the penalty for falling away under that condition, as given in Heb.6:8, "But that which beareth thorns and briers is rejected, and is nigh unto cursing; whose end is to be burned."
So don't be silly in thinking that applies to the Body of Christ as anything other than a strong warning to stay in Christ Jesus; it's especially for those who have a calling from God as a chosen one, and have evidence of God's works to prove it.
I will respond more later as i need to get over to the hospital and pick up some x-rays.
But you said, "And you just don't get it about Abraham's household either. Hagar and Ishmael were cast out... of Abraham's household, which as an allegory is the opposite of your idea."
Hagar was not mercilessly totally cast off of Abraham as you say. She did and her descendants did receive some mercies of him. You are overlooking those events. And this all corresponds perfectly to what happened to Jerusalem in the first century, for that Jerusalem and her descendants are yet being shown mercy of the greater Abraham, this by virtue of the promise that in Abraham all of the nations of the earth would be blessed.