The one who has been born of God loves others (4:7-8). John is expressing the second greatest commandment, love for one’s neighbor. This is drawn from Jesus’s own teaching, but it is also part of Second Temple period Judaism. Love for God and love for one’s neighbor often expresses a summary of the whole law.

The love of God is clear when he sent his son into the world (4:9). It is important to clarify at the beginning of this section on God’s love that God’s love is not at all like the human emotion of love. John Peckham asks, “Does God’s love include affection, desire, or enjoyment?” In other words, his is love merely agape love, or can he experience eros, enjoyable love? In order to make this question make sense, Peckham includes a chapter on the meaning of agape and eros in order to avoid confusion caused by popular preaching on God’s love (The Love of God: A Canonical Model (IVP Academic, 2015).
As with most theological ideas, to say God’s actions in sending Jesus as an atoning sacrifice is “love” is to use an analogy so humans can understand something of God’s character. God’s love is something like our love for a spouse or a child, but God’s love is exponentially greater and more complex. In fact, the love of a parent for a child is a better analogy than romantic love between spouses. There are many examples of human parents sacrificing everything so that their children might be safe.
The love of God is demonstrated by God’s gift of his son as a propitiation for our sins (4:10). Sending the son into the world was not a response to humanity’s desire for a relationship with God. John is clear, it is not that we loved God!
John called the death of Jesus an atoning sacrifice in 2:2. A propitiation (ESV) or “atoning sacrifice” (NIV) is a sacrifice which turns away the wrath of a god. The noun (ἱλασμός) and related words are used in the LXX for the Day of Atonement (Lev 25:9) In the Old Testament the word and its cognates almost always refer to appeasing the wrath of God (Lev 1:4, for example).
In the Greco-Roman world, a god might be calmed by human or animal sacrifice, but other rites of purification or prayers were also common. Sometimes ritual dances and games dedicated to the god could please the god and turn aside wrath. What is remarkable about the atoning sacrifice in 1 John is that God himself makes the sacrifice, and God himself is the sacrifice! No god in the ancient world would act on behalf of his worshipers in this way. Rather than vent his wrath on his creation, God demonstrated his love for his creation by turning aside his wrath himself.
John is not far from Paul’s words in Romans 5:6-8. While we were powerless to help ourselves and in a state of enmity with God, Paul says God sent his son to die for us. The ultimate demonstration of God’s love is therefore the ultimate self-sacrifice of his own son in order to provide forgiveness to people who would never know or care that this gracious act even happened!
John tells his readers they ought to love one another, but they cannot begin to love one another until they have accepted God’s gracious gift of forgiveness. By experiencing this gracious act of love from God we then are able to demonstrate that love to others.
What are the opponents teaching about Jesus? The usual suggestions include Docetism (Jesus only appeared to have real flesh since human flesh is by nature evil), Cerenthus (the earthly Jesus is different than heavenly Jesus), or even a teaching that Jesus was flesh, but his flesh was important for our salvation (Von Wahlde, Epistles of John, 142-43). The problem is the later descriptions of these classic Christological heresies fit what John says. Perhaps it is better to take this false teaching about Jesus John is concerned about as similar to these later rejected Christologies.
It is also possible the opponents are well-meaning Christians who are genuinely trying to teach accurately about Jesus, but they sincerely disagree with John about who Jesus was. In the Gospels themselves it is clear even the disciples were not exactly clear on who Jesus was or what he came to do. When Peter finally confesses Jesus as messiah, Jesus tells Peter the purpose of the messiah is to go to Jerusalem to suffer and die. Peter rebukes Jesus since this is not what he expected messiah to do! When the false prophets “go out into the world” they have demonstrated their rebellion from God. In John’s Gospel the world is a place of darkness and it is the domain of Satan.
In either case, these traveling teachers would have had limited access to Scripture. It is unlikely any of these small congregations would have even small portions of the Old Testament in Greek. They may have had limited copies of some of Paul’s letters and perhaps other communiques from John. These traveling teachers would therefore rely upon the Holy Spirit to call to mind Scripture which they had memorized and their teaching was done “in the Spirit.”
Applied to a theological idea like Jesus is the Messiah, the opponents certainly know this is what John has said in his Gospel, but they deny that it is valid and they reject that teaching as having any impact for their lives. I might read an essay on the importance of going to confession and doing penance in the Catholic tradition. I can hear the words and understand what they are saying, but I will deny that it has anything to do with me as a Protestant.