Why Mourn Death If Birth to Eternal Life?

Because death reminds us of the impact of sin and thus the painful separation, even though temporary, that death brings into human relationships.

Consider that Jesus mourns the loss of Lazarus, even though he knew that, as the omnipotent Incarnate Word, he was going to raise Lazarus from the dead shortly thereafter (John 11:32-36).

So, as is typical of Catholicism, death is a both/and, a time of mourning and yet also hope for eternal life, not an either/or.