I have read what was written on the website about why the Jews rejected God, but I remain confused as to why this occurred. Are you able to make it clearer? Using passages from the Bible does not explain this, at least I have not read it. What I have gathered, by reading, is that they didn't agree with what was being preached, as it didn't conform to their ideals.
This is a subject that has intrigued me for many years. Is it possible that the Jews got what was coming to them throughout history because of this failing? I am no academic, but it seems that many such people can argue and debate these questions for hours, and still be no wiser. A little enlightenment would be greatly appreciated.
You almost answered your own question. All you are lacking is quoting of Scripture and maybe one or two points.
Stiff-necked Rebellious People
Israel is known for their rebellion towards God, ""You men who are stiff-necked and uncircumcised in heart and ears are always resisting the Holy Spirit; you are doing just as your fathers did. Which one of the prophets did your fathers not persecute? They killed those who had previously announced the coming of the Righteous One, whose betrayers and murderers you have now become; you who received the law as ordained by angels, and yet did not keep it." Now when they heard this, they were cut to the quick, and they began gnashing their teeth at him" (Acts 7:51-54). The response of the Jews at the rebuke given by Stephen is that they again did just as their fathers did, and they in turn stoned Stephen, a prophet of God.
The legacy of Israel since coming out of Egypt was the same as it was in Stephen's day. They have always been a stiff-necked people from the start of the Exodus (Deuteronomy 9:6-24). You are correct in that they wanted God to be a god in their own image. The Hebrews had brought false gods with them and even made a golden calf to represent the true God (Acts 7:41-43; Amos 5:25-26). Consider that the Pharisees scoffed at Jesus' teaching of serving God and not wealth (Luke 16:13-15). What they showed was that they loved the idea of being God's people, but only when it was convenient. They did not want to commit to the way of righteousness. Their love and zeal was only for their own desires and traditional ways (Matthew 15:1-9; Romans 10:2-3).
God sent Warnings and Prophets
Many verses that talk about Jews and all the chances they were given, here are just a few,
"Yet He sent prophets to them, to bring them back to the LORD; though they testified against them, they would not listen" (II Chronicles 24:19).
"Since the day that your fathers came out of the land of Egypt until this day, I have sent you all My servants the prophets, daily rising early and sending them. Yet they did not listen to Me or incline their ear, but stiffened their neck; they did more evil than their fathers" (Jeremiah 7:25-26).
"Because they have not listened to My words,' declares the LORD, 'which I sent to them again and again by My servants the prophets; but you did not listen,' declares the LORD" (Jeremiah 29:19).
"Also I have sent to you all My servants the prophets, sending them again and again, saying: 'Turn now every man from his evil way and amend your deeds, and do not go after other gods to worship them. Then you will dwell in the land which I have given to you and to your forefathers; but you have not inclined your ear or listened to Me" (Jeremiah 35:15)."But they became disobedient and rebelled against You, And cast Your law behind their backs And killed Your prophets who had admonished them So that they might return to You, And they committed great blasphemies" (Nehemiah 9:26).
Consider that you warn someone thousands of times (which God did do), you tried every possible mode of correct discipline and are consistent with punishment and warnings, "You shall not worship them or serve them; for I, the LORD your God, am a jealous God, visiting the iniquity of the fathers on the children, on the third and the fourth generations of those who hate Me" (Exodus 20:5), yet over a thousand or more years they still are rebellious and will not turn to God (Matthew 23:34-39). That is the Jews in a nutshell: a people who could not in the end learn from their own mistakes.
God uses Israel's rejection for His salvation of mankind
"I say then, they did not stumble so as to fall, did they? May it never be! But by their transgression salvation has come to the Gentiles, to make them jealous" (Romans 11:11). The purpose of the Jews rejecting God is because He used the stubbornness of the Jews in their own free will to have salvation brought by the crucifixion of Christ.
"Men of Israel, listen to these words: Jesus the Nazarene, a man attested to you by God with miracles and wonders and signs which God performed through Him in your midst, just as you yourselves know -- this Man, delivered over by the predetermined plan and foreknowledge of God, you nailed to a cross by the hands of godless men and put Him to death. "But God raised Him up again, putting an end to the agony of death, since it was impossible for Him to be held in its power. ... "Therefore let all the house of Israel know for certain that God has made Him both Lord and Christ -- this Jesus whom you crucified." Now when they heard this, they were pierced to the heart, and said to Peter and the rest of the apostles, "Brethren, what shall we do?" (Acts 2:22-24, 36-37).
"So when they heard that, they raised their voice to God with one accord and said: "Lord, You are God, who made heaven and earth and the sea, and all that is in them, "who by the mouth of Your servant David have said: 'Why did the nations rage, And the people plot vain things? The kings of the earth took their stand, And the rulers were gathered together Against the LORD and against His Christ.' "For truly against Your holy Servant Jesus, whom You anointed, both Herod and Pontius Pilate, with the Gentiles and the people of Israel, were gathered together "to do whatever Your hand and Your purpose determined before to be done" (Acts 4:24-28).
Even though Jew and Gentile intended harm towards God, He turned it around and used the death of Jesus for all of mankind for good. God had foretold of this plan and how it would happen many years before,
"The God of Abraham, Isaac and Jacob, the God of our fathers, has glorified His servant Jesus, the one whom you delivered and disowned in the presence of Pilate, when he had decided to release Him. "But you disowned the Holy and Righteous One and asked for a murderer to be granted to you, but put to death the Prince of life, the one whom God raised from the dead, a fact to which we are witnesses. And on the basis of faith in His name, it is the name of Jesus which has strengthened this man whom you see and know; and the faith which comes through Him has given him this perfect health in the presence of you all. And now, brethren, I know that you acted in ignorance, just as your rulers did also. "But the things which God announced beforehand by the mouth of all the prophets, that His Christ would suffer, He has thus fulfilled. Therefore repent and return, so that your sins may be wiped away, in order that times of refreshing may come from the presence of the Lord; and that He may send Jesus, the Christ appointed for you, whom heaven must receive until the period of restoration of all things about which God spoke by the mouth of His holy prophets from ancient time. Moses said, 'The Lord God will raise up for you a prophet like me from your brethren; to Him you shall give heed to everything He says to you. And it will be that every soul that does not heed that prophet shall be utterly destroyed from among the people.' And likewise, all the prophets who have spoken, from Samuel and his successors onward, also announced these days. It is you who are the sons of the prophets and of the covenant which God made with your fathers, saying to Abraham, 'and in your seed all the families of the earth shall be blessed.' For you first, God raised up His Servant and sent Him to bless you by turning every one of you from your wicked ways" (Acts 3:13-26).
Consider Joseph's statement about the evil his brothers caused him; yet, God's hand is seen in guiding Joseph and saving people through his brothers' sin (Genesis 45:4-9; 50:15-20).
What was the purpose of the Jews to reject God? It was to bring about salvation to the world, but God still showed them lovingkindness regardless of their sins. Knowing they were evil and not willing to follow Him, God used what they meant for evil and turned it around for His good pleasure. Even with them crucifying the Savior of the world, Jesus Christ, they still are told they have a chance to repent, "For you first, God raised up His Servant and sent Him to bless you by turning every one of you from your wicked ways" (Acts 3:26).