Claim: Christians are being arrogant when they claim Jesus is the only way to God.

We can be arrogant at times, but this is not our claim, but Jesus'.

Christians can indeed behave arrogantly: particularly when we fail to demonstrate in actions towards others the love and humility of our Lord and Master. We can all be arrogant at times.

However the claim that Jesus is the only way to God is not our claim.

Jesus Himself says He is the only way:

“Do not let your hearts be troubled. You believe in God; believe in Me as well. In My Father’s house are many rooms. If it were not so, would I have told you that I am going there to prepare a place for you? And if I go and prepare a place for you, I will come back and welcome you into My presence, so that you also may be where I am. You know the way to the place where I am going.

“Lord,” said Thomas, “we do not know where You are going, so how can we know the way?”

Jesus answered, “I am the way and the truth and the life. No one comes to the Father except through Me. If you had known Me, you would know My Father as well. From now on you do know Him and have seen Him.” John 14:1-7

And Jesus Himself says that He is the only one for whom it is any use losing our lives:

Then Jesus told his disciples, “If anyone would come after me, let him deny himself and take up his cross and follow me. For whoever would save his life will lose it, but whoever loses his life for my sake will find it. For what will it profit a man if he gains the whole world and forfeits his soul? Or what shall a man give in return for his soul?” Matthew 16:24-26

Christ Carrying the Cross: Titian. The painting was acquired in Italy between 1637 and 1642 by the Marquis of Leganés, who gave it to Isidoro Aliaga, the Archbishop of Valencia. In 1666 it is documented as belonging to the Spanish Royal Collections and entered the Museo del Prado. https://commons.wikimedia.org/wiki/File:Titian_-_Christ_Carrying_the_Cross_-_WGA22841.jpg public domain