You seem to be constructing an argument like "if suffering is not immoral, then you must also think that torture is moral". That's a straw-man argument. It is a perfectly valid position to assert that inflicting suffering is morally wrong while at the same time rejecting that all suffering is morally wrong.

When someone says that something is not immoral (or evil), they can be arguing to things: either it is moral, or it is amoral (i.e. is not affected by qualifications of morality). The GP is arguing the latter: that, in the context of nature, suffering is an unavoidable consequence of competition for life. Is the lion evil for targeting the weakest wildebeest? Is toxoplasmosis evil for disrupting the fight-or-flight response of its host?