Jesus is God. (John 1, John 8:58)
God is Life. (Deuteronomy 30:19, John 14:6)
God is holy, set-apart and sinless. (Isaih 6:3, 2 Corinthians 5:21, James 1:13)
Therefore, when we sin, we remove ourselves from the presence of God.
If we die in that state, having not repented and asked God for forgiveness, we reject life itself.
It is no wonder the penalty of sin is death, since the absence of life is death.
“For the wages of sin is death, but the free gift of God is eternal life in Christ Jesus our Lord.” – Romans 6:23