This is why Jews are Jews and not Christians, among many other reasons, but I don't think I ever really learned the historical reasoning for the rejection at the time of his death. Whether you believe Jesus is the son of God, he was a real person.
I just don't understand how and why exactly they didn't believe he was the son of God, and how they managed to survive for so long not believing it.
Not quite. Rome lasted for more than a millennium. And the Western Empire was troubled long before Christianity became the official state religion.
If a nation gets threatened from the outside and destabilized from the inside because of retarded religious insanity it becomes impossible for it to defend itself from invaders. Which is what happened.
Christianity becoming the official state religion and every non-Christian religion being outlawed and persecuted made it impossible for Rome to stabilize again and was the final killing blow.
That old Gibbon thesis has long been discredited.
So why did the Eastern Roman Empire, which was more Chrisitan than the West, survive?
It didn't. That's why Constantinople is called Istanbul.
It survived for more than 1100 years after Constantine. Was there ever an empire that lived longer?