Why isn't it good enough to believe that Christ is the Savior in order to be considered Christian?

My religion, The Church of JESUS CHRIST of Latter-Day Saints, believes that Christ is the Son of God and the Savior of the World and that He died for us, atoned for our sins, and was resurrected. Why isn't that belief sufficient for us to qualify as Christians? I've heard the argument that Islam mentions Christ, but isn't Christian and that's quite a faulty comparison. Islam doesn't worship Christ or believe that He is the Savior or the Son of God! So, HOW can ANYONE compare us to Islam? I've also heard the argument that the Devil and the demons believe in Christ, but like I mentioned before, they don't WORSHIP, HONOR, or REVERE Christ as their PERSONAL SAVIOR! In order for someone for to non-Christian, they have to be INTENTIONALLY rebelling, OPENLY denying, and WHOLEHEARTEDLY antagonizing Christ! A non-Christian must NEVER have good intentions toward Christ. But, our Church has NOTHING but good intentions and we don't antagonize, rebel against, or deny Him. Can anyone explain this to me?