On Nietzschean criticism of Schopenhauer's Will-to-live

Nietzsche criticizes the concept of will-to-live in Schopenhauer's philosophy by the following arguments:

1. If someone does not exist, s/he cannot will to live.

2. If someone exists, s/he exists already, so will-to-live is meaningless in that case.

The first argument is very straightforward and not in dispute in any meaningful way. The second argument sounds clever and profound at first sight, just like much of Nietzsche's works. On further analysis, however, this argument reaches a conclusion the likes of which can in fact only be found in mental institutions.

Can we stay alive if we don't do anything? Like the adage "Freedom isn't free" after 9/11, to be alive isn't free, either. One needs to eat, breathe, drink, etc. As one can see, a will-to-continue-to-live, or will-to-live in short, permeates through every single person's life. One just does not stop breathing or eating since "s/he is already alive anyhow." In short, the fact that will-to-live actually points at a real phenomenon in living people cannot be denied by clever word plays.