As I was taught, god offered up his son (which he loved) to be brutally killed to save his human creations (which he also loves)

Well he offered up his son for the whole creation not just humans, but yeah.

from original sin - a transgression that none of us has actually committed.

I don't know how much background you have in this, but you may be aware that the subject of original sin is much controverted. I think it helps to understand that the biblical authors viewed sin (and the closely related areas of death and decay) not just as something bad that people do, but also a something of a force that stands behind those bad actions and which enslaves humans and the rest of creation. So while sin includes human choices to disobey god, etc. it is not wholly reducible to them.

You also must understand that the death of Jesus functions as the climax of the story of Israel. This whole connection is made most fully by Paul, but I will try to summarize it here. Israel was tasked with a commission to be a 'blessing' and 'a light' 'to the nations,' and they were given the law as a means to help them by the people who could fulfill that commission. But because the people and the world were enslaved to sin or 'in bondage to decay.' So the law tries to give life, but it can't (not because there was something wrong with the law, but because there was something wrong with the people). Instead the law has the effect of magnifying the sin that is there. It paints a bright line and makes it very clear that the people constantly don't measure up to it. So, Paul says, the law 'multiplies transgressions.' And the fact that the law is given to Israel focuses this transgression this sin on Israel.

Now this all seems like it throws a wrench in God's plan, but Paul (we are now in Romans 7-8 territory) says that God was actually setting a trap, because Israel's Messiah is Israel in person. He is the one who represents Israel; he is the Israelite. So when all the powers of sin, death, and decay are fully focused on Israel, God sends the Messiah who is Israel's representative so that sin, death, and decay may ultimately rest on him and be condemned through his death. God then vindicated his representative by raising him from the dead, enacting the defeat of death and the other powers which had enslaved the world and launching the new creation.

So if we apply this to your questions, it is not as though all humans are responsible for Eve eating a piece of fruit, and the 'son' in question here is not just any son. He is God's son who is Israel's Messiah, so his life and death have specific meanings and consequences.

That is some dense theology I've tried to summarize, so it might make even less sense than before, but let's talk about it.