Many does not mean not all. Jesus is the Savior of the whole world...of all men.
You are setting a fire to the other scriptures.
1 John 2:2 He is the atoning sacrifice for our sins, and not only for ours but also for the sins of the whole world.
1 Timothy2:3-6 This is good, and pleases God our Savior, who wants all men to be saved and come to a knowledge of the truth. For there is one God and one mediator between God and men, the man Christ Jesus, who gave himself as a ransom for all men—the testimony given in its proper time.
1 Timothy 4:10 (and for this we labor and strive), that we have put our hope in the living God, who is the Savior of all men, and especially of those who believe.