Believing on Christ as God

Why does it matter if people believe that Christ is God or not? Does Christ being God take away from Him being a Man? Why must you not only believe Christ is God but also believe He was a Man in order to know Who He is and what He accomplished as the God-Man? How does the vehemence toward Christ pertain to the heart of depravity? Can indifference be just as much an enmity against God as outright hatred?