They haven't made the same claims though. If you read the Quran and study the events around its revelation and the state of the Abrahamic religion that came before it you would understand why it was needed. Christianity has been completely hijacked and weaponised and the Bible filled with hundreds of direct contradictions, the words of Jesus (pbuh) were never even recorded directly, only through John etc. because as he said he only came for the lost sheep of Israel and he foretold the prophet Muhammad (pbuh) coming. The lineage of Abrahamic religions is a perfectly straight line and as more and more people discover the truth, they convert.

Islam is the most converted to religion in the world by far because no matter how much let the same media they claim to hate brainwash them about it, the truth always prevails.