Why did Jesus die since he did no sin?

There are two reasons why we die:

1. We sin, and the “wages of sin is death” (Romans 6:23).
2. We inherit mortality (Romans 5:17).

Since Jesus did not sin (Hebrews 4:15), only the second of these applied to him. That is, he inherited mortality because he was human.

However, because he did not sin, and lived a faithful and righteous life, it was not right for him to remain dead:

God raised him up, loosing the pangs of death, because it was not possible for him to be held by it. (Acts 2:24)