Shared ground
Paul explains what drives and directs his conduct: “the love of Christ” presses him forward (explicit). This inner pressure is tied to a settled conclusion he shares with his readers: one person (Christ) died “for all,” and Paul draws a connected result: “therefore all died” (explicit).
Paul then states the purpose of Christ’s death in moral, directional terms: Christ died “for all” so that “those who live” would no longer live “to themselves” but “to him” (explicit). Christ is identified as the one who both “died and rose again” for their sake (explicit). The passage presents Christ’s death-and-resurrection as creating a new center of loyalty and aim (inference from the purpose statement).
Where interpretation differs (only where needed)
1) “The love of Christ”
Some read it mainly as Christ’s love for people (the love shown in his death). Others read it as Paul’s love toward Christ. The first fits the immediate logic (“one died for all”), but the phrase itself can be heard either way.
2) “For all” and “all died”
Some take “for all” to mean every human being without exception. Others take it as “all” within a defined group in view (for example, the community that shares this “settled judgment,” or those who end up being described as “those who live”). Likewise, “all died” is read by some as a statement about humanity’s shared condition; others as a statement about a representative death that counts as the group’s death in relation to Christ.
3) “Those who live”
Some interpret “those who live” broadly (all people are given life in some sense through Christ). Others interpret it more narrowly (those who now live in the new life connected with Christ’s death and resurrection). The text itself links “those who live” to the purpose of Christ’s death and to a changed allegiance.
Why the disagreement exists
Paul uses compact, interconnected claims (“one died for all… therefore all died”) without spelling out all the steps between them. He also uses repeated, flexible words like “all” (all) and “died” (died) that can be understood in more than one scope. Finally, the phrase “love of Christ” can grammatically point either to Christ’s love or to love directed toward Christ, and the immediate context strongly emphasizes Christ’s act while leaving the phrase open.
What this passage clearly contributes
This passage supplies Paul’s core motive-language: Christ’s love is not only a feeling but a driving force that shapes choices (explicit). It also states an intended outcome of Christ’s death: a transfer of life-aim from self as the center (“to themselves”) to Christ as the center (“to him”) (explicit). And it binds that transfer to the combined reality of Christ’s death and resurrection “for their sake” (explicit), establishing that Christian moral direction is rooted in what Christ has done, not in public image or self-advancement (inference consistent with the surrounding context in 2 Corinthians 5).