Two things are usually confused here: an arrogant attitude and an exclusive claim.
Every worldview makes exclusive claims
This includes the worldview that says "no one religion is uniquely true." That is itself a particular metaphysical claim that excludes all the traditional religions. Religious pluralism is not a humble middle ground — it is one more contested position. Truth, by definition, is exclusive of error.
Christianity does not claim that Christians are better than other people
It claims, in fact, the opposite — that every person needs grace they cannot earn (Romans 3:23). The exclusivity of Christ is not the exclusivity of a club. It is the exclusivity of a hospital: only one cure works for the universal disease, and that cure is offered to everyone freely.
The claim rests on a specific event
Jesus said, "I am the way, the truth, and the life. No one comes to the Father except through me" (John 14:6). This is either true or false. The Christian's reason for accepting it is not feeling but evidence: the historical Resurrection of Jesus (1 Corinthians 15:14). If that did not happen, Christianity is false. If it did, the exclusive claim is not arrogance — it is news.
Genuine love requires truth-telling
A doctor who pretended every treatment was as good as every other would not be humble. He would be irresponsible.