There are about 40,000 Christian churches world-wide. Protestants rejected the Catholic Church. That eliminates most of the 40,000. The Catholic Church rejected the authority of the Priesthood by eliminating the two priesthood orders of Melchizedek and Aaronic (Levitical). The Priesthood is key because the Priesthood is the authority and power of God which made the heavens and the earth. It's God's Priesthood (authority and power) given to man to do His work on earth. As a Catholic Priest once said in a talk to members of The Church of Jesus Christ of Latter-day Saints, "Protestants have no leg to stand on because they came out from us while we had the authority and truth. Therefore, they apostatized and have no claim of authority and the church of Jesus Christ. It's either the perpetuation of the Church from former days or the Restoration of the Church in these the Last Days."
Your challenge is the same argument Jews had in the time of Jesus Christ when he challenged the authority of the Rabbis, Sadducees and Pharisees. He also mostly silently and indirectly challenged the authority of the Roman gods as well. In fact, he rejected them all and gave the people who followed him a new commandment, taught the true religion and organized a new Church. He called Apostles, prophets, evangelists, teachers, preachers and so on to run the Church including bishops in other cities. Apostasy isn't new. Ancient Israel had challenges with it that caused 10 of the tribes to be lost forever until the second coming of Christ. They lost their authority.
How does the Church look at other sects of Christianity? We don't completely reject them as they reject us. We believe that all people have a right to believe the way they want to. When they confirm righteous faith in God through prayer, we believe their prayers can be answered. That they can have personal relationships with God. They can be blessed in righteousness. They can perform their rituals of baptism and other ordinances the way they want to. What we bring to the table is the authority and power of the Priesthood with the correct administration of the ordinances of the Priesthood. The authority of the Priesthood must come from God, by God and those he has in the past ordained. Joseph Smith received the Priesthood from Peter, James and John who received their Priesthood authority from Jesus Christ. From that point on, members have received that same Priesthood from those in genealogical order over the past about 190 years. With The Book of Mormon, the fulness of the Gospel has been restored in these the latter days.