If you believe that Jesus is unique amongst all human beings, you already believe in election, and you already believe in what many consider to be the most offensive part of the doctrine: that some are chosen whilst others are not. If Jesus is the chosen, nobody else is. Already you have the scandal of particularity - that God deals with this particular person, in this particular way which is not accessible to the rest of us. Belief in Jesus as the Christ necessitates this.
But what is offensive to many about the Calvinist doctrine is that it is unconditional election; God's choosing does not depend on anything in the recipient. This, too, can be traced Scripturally to Jesus (although I don't know whether Calvin ever did this, and I have reason to doubt it). Early church theologians, following the witness of Scripture, spoke of the anhypostasis of Jesus' human nature, which was just an invented Greek word to say that the human nature of Christ had no existence apart from its assumption into union with the divine nature of the Son of God. In other words, there weren't a bunch of humans sitting on a shelf and God chose one he liked; rather, in willing the incarnation, God willed that this particular human be. He wasn't the elect of God because of anything he had done. Everything he was and did flowed from his being the elect of God.
Which brings us to the aspect of election which doesn't get enough airplay in Calvinist circles: the elect are chosen for the sake of others. Jesus is the elect in order to gather in the elect. Until such time as that circle of election is complete, election always means election to service, because that is what it meant for Jesus. And since Jesus was chosen in order to bring salvation to the world (without limits known to us), we cannot ever assume that anyone currently standing outside the circle belongs there. Election means service.