The love of God is demonstrated in his unconditional election of his saints.
The doctrine of the love of God had always confused me before I understood it in light of limited atonement. In the past, I assumed that God had a homogenous and monotone love for all creation and all humans alike; that it did not matter whether someone was a sinner on his way to hell, or a saint who had been redeemed by the blood of Christ. I thought that the love, that we had coined the "agape" love of God, was a single blob of love dumped on everyone at exactly the same time, in exactly the same measure and mode.
Here's what confused me:
1. God has agape love for me
2. God has agape love for the one going to hell
3. The love of God can result in the eternal damnation of the soul
4. The love of God is therefore not a saving love
5. The agape love for me is weak, undirected, and indistinct
The implications would be:
1. God's love for me is nothing more than a general positive disposition that God has for all his creatures, including slugs and microorganisms.
2. God's love for me is not what saved me, for there are people loved by God who are not saved.
3. There can be no true comfort nor security in the love of God.
Now, the rebuttal is that people go to hell because they reject the love of God.
First, let's remember what hell is. It is everlasting torment and torture without possibility of relief, the result of the wrath of God against sinners. How this reality and God's superabundant love can be given to the same soul, I do not know. This seems more like the outworkings of hate than of love.
Therefore, if people receive this hate as a result of their rejection of love, then God's love is no longer unconditional, but conditional.
The solution to this problem is to understand the love of God as the Bible presents it. A sermon by John Piper helped me to understand it, from Malachi 1:2-3,
I have loved you," says the LORD. But you say, "How have you loved us?" "Is not Esau Jacob's brother?" declares the LORD. "Yet I have loved Jacob but Esau I have hated. I have laid waste his hill country and left his heritage to jackals of the desert."
How does God demonstrate his love? By choosing Jacob over Esau. By choosing Israel over the nations. By choosing the saints over the sinners. As it is written in Romans 8:38,
For I am sure that neither death nor life, nor angels nor rulers, nor things present nor things to come, nor powers, nor height nor depth, nor anything else in all creation, will be able to separate us from the love of God in Christ Jesus our Lord.