The thing is, God never stopped loving us. Even when we were in our sins, He loved us. When Christ died on the Cross, that was God showing His love for us. His love has no limit or end, which is why He chose to offer us an alternative to hell than just leaving us all to our deserved fate. It's why it's grace, a gift of salvation from a Father who loves each and everyone of us, but, not everyone loves God. So, they choose their own fate, which unfortunately ends in eternal torment for their unfaithfulness. Rejection of the work of Christ on the cross is what I imagine to be, a big slap to the face of our creator. He didn't have to do anything for us, heck, He didn't have to make us at all! Yet He did, and He chose to provide a way to eternal life rather than eternal damnation.
In order to understand why hell exists, we have to understand something about the nature of sin. Sin is a stain, it is an offense to God, it is an abomination in His eyes. To sin we die, the wage of sin is death, so one who dies in their sinful state dies as an enemy of God. It is due to sin that destruction is necessary. On the Cross sin was defeated once and for all for everyone who called upon Christ as Lord, because in Him it was defeated by His Holy blood, each and everyone who calls Christ Lord is washed clean of sin. Though we still sin, we have been redeemed. Just as Christ crossed over from death to life, so shall we all who revere Him and love Him. It's hard to put it into words but I'll try.
Think of radiation poisoning. It damages the body, destroys the cells, and ultimately the contamination kills you. Sin is like radiation poisoning of the soul. It kills the spirit. Temptation ensnares, acting upon it trespasses, and when it contaminates, it slays the person. Yet the body lives on, but it's more akin to a zombie from a spiritual point of view. An animated being just barely above an animal in terms of functionality, sentient of course. I'm not saying everyone is no better than an animal, God knows I'm as guilty of sinning as the next person, it killed me too. But in Christ, I was brought back to life by the power of God and made a new creation. Sin no longer has a hold on me, though I may still succumb to it. But my soul is guarded by the Lord and I am in His hands forevermore, though my actions will be judged before the seat of Christ, but so will all believers actions be. It's just how it goes, but even then, what we've gained is immeasurable. The Kingdom of Heaven is now open to us? We could never deserve it, yet God freely gave it to us. So it's not as though God is toying with anyone, He's not the tempter. God tempts no man. God convicts sin, for because He is Holy it must be punished. But, He is also loving, and merciful, so He arranged a way that sinful man can be justified before Him, and we are for the sake of the Son. Because Christ is Holy, those who take part of that salvation in Him are also counted as Holy, because we die to ourselves and live in the Son. Because the Son is righteous, we too are now seen as righteous, because we are now with the Son. Not by our own effort, because our efforts were ruined by the contamination of sin, but now we can do something useful for once, because if we do any good, it is God at work in us that does the good, though we are the agents of those works. God never stopped loving you, and He never will, but due to the abomination of sin, His Holiness demands it be punished, or alternatively, atoned for in Christ. It's not a cop out, sin demands death. So Christ died for the sins of all, though He Himself never sinned. So it is in this way that we are made right before God, and why we should always give thanks to our Lord Jesus Christ.