The reason is because God is perfect love, but God is also simple. That means all His attributes are present and none can be divided from the others. So He is loving, just, truthful, faithful, patient, and many other things all in perfect balance.
Did God not say He would exact eternal punishment upon sinners who refuse to repent? He is truthful, so He could not lie about this.
Will God do it? He is faithful, so He keeps all His promises.
Is God just? Then He must punish wrongdoing.
Is this punishment a just punishment? For one, is there an alternative path He could take to achieve His goals that enhances His love without diminishing His other attributes? God is infinitely wise so must have considered every option. If Jesus in the Garden of Gethsemane asked His Father if there was another way besides the cross and this infinitely wise and loving God when addressing His sinless Son whom He loves said, "No", then it is certain that there is no better way that ensures the salvation of as many as can be saved. If God is wise and loving and truthful and declares that this punishment shall go forward, then it is just.
You say, "I didn't ask to be here..."
You turn things upside down,
as if the potter were thought to be like the clay!
Shall what is formed say to the one who formed it,
“You did not make me”?
Can the pot say to the potter,
"You know nothing”?
Paul in Romans said,
19 One of you will say to me: “Then why does God still blame us? For
who is able to resist his will?” 20 But who are you, a human being, to
talk back to God? “Shall what is formed say to the one who formed it,
‘Why did you make me like this?’” 21 Does not the potter have the
right to make out of the same lump of clay some pottery for special
purposes and some for common use?
22 What if God, although choosing to show his wrath and make his power
known, bore with great patience the objects of his wrath—prepared for
destruction? 23 What if he did this to make the riches of his glory
known to the objects of his mercy, whom he prepared in advance for
glory— 24 even us, whom he also called, not only from the Jews but
also from the Gentiles? (Romans 9:19-24)
If we harbour ideas that the punishment is too great for the crime, yet God is just in punishing sin as He does, it must be because we grossly misjudge the severity of sin. Jesus died to pay for that sin, if only we accept his work by having faith in him. God does not take sin lightly. He paid the ultimate price. Consider the severity of sin to be equal to the payment made to eriadicate it. Infinite God offered His Son, of infinite worth, to fix the problem. That means that sin is far more deadly than we can possibly imagine. Our inability to see that or accept it is a measure of our spiritual blindness.
Yet that is not the only reason God punishes us for sin! A measure of the suffering that we endure is really a message from God. Jesus suffered on behalf of others. Such character and love is highly valued by God. God wants all His children to possess exceeding virtue. He wants us to become more like Jesus. To do that, we must suffer as he did so that our lives may produce the fruit of righteousness. The greatest faith is displayed by those who trust in God's goodness in the midst of great suffering. Such a person is a witness to all around them of a miracle. Only a miraculous faith can persist in the midst of suffering. This is what Job displayed to the people around him. Job's reward was that the longest single speech in the Bible that God ever delivered to any person, He spoke to Job.
As a personal example, years ago I several times visited a woman named Janet in a nursing facility who suffered horrible pain from rheumatoid arthritis. She was a believer in Jesus Christ and continued to share her faith with all who visited her. After leaving her room after my first visit, I was overcome with tears and sobbing. But a half hour later, the tears were replaced with peace, and then ecstatic joy. The joy stayed for an entire week. A few months later I attended her funeral. One of the people there said something I will never forget: "When you were with Janet, it was like the Holy Spirit was pouring out of her." Amen. After that meeting with Janet, I was delivered from over a decade of depression. Why do we suffer? Some of that suffering, if we believe that God loves us no matter what, becomes spiritual power to shower blessings on the people around us. Broken but faithful people are channels of God's love.
12 My command is this: Love each other as I have loved you. 13 Greater
love has no one than this: to lay down one’s life for one’s friends.
14 You are my friends if you do what I command. (John 15:12-14)
God's desire is that we be people who love. Love means laying down your life for the ones you love.
For whoever wants to save their life will lose it, but whoever loses
their life for me will save it. (Luke 9:24)
The ones who go to Hell try to save their life by not loving others in a costly way. The ones who go to heaven are willing to lose their life to help the ones they love. The responsibility is ours. God shows us the respect to accept our decision as people with free will.
In a comment, the OP asks:
Why not just leave those who don't want to follow him alone?
What do you suppose being alone for eternity would be like? In The Great Divorce, C. S. Lewis took a stab at it. His shining example was Napoleon, on a planet by himself, endlessly arguing with himself over who was to blame for his defeat. Lewis showed people arriving in Hell. At first they hang out with their former family and friends, but with no light of goodness from God, every good part of the people they knew on earth is gone, they figure it out, and eventually can't stand being near each other. Every person in hell slowly moves away from every other person until they are completely alone.
We have a conceit that we are all in this world together: good people, bad people, good things, bad things, God and Satan. We can imagine putting up a fence and separating the good from the bad so that each would leave the other alone. What is it like to exist in a world without God? A world with no goodness? A world of comlpete loneliness?
What happens to prisoners in our world that are put in solitary confinement for too long? They go crazy. The emotional pain of being separated from human contact grows until it exceeds the worst physical pain. It is a pain without hope of ever diminishing. That is Hell. The only antodote is to be in the presence of God, which they have rejected. There are no good things apart from the presence of God.
Lewis shows a woman from Heaven going to visit her husband at a waypoint in the middle. She tries to convince him to come to heaven and share her joy. He is mad at her for not sympathising with his pain and torment. However, she is wrapped up in the beatific vision. She can no longer experience sadness or pain, only joy. Her husband cannot guilt her by his old put downs into feeling shame and powerlessness. He cannot cut her down and it infuriates him. He can no longer oppress or control her, the thing he desires more than happiness. So he leaves and returns to hell. His every inclination is to do to the saints things which God will no longer permit. The frustration at having a sinful will opposed in all its actions forever is exhausting and agonizing. That is hell.