The main enquiry about the quote could be what made him (or would make anyone else) think that life was a great mistake?
And why would he think that this should necessarily apply to everyone?
The Merriam Webster dictionary defines a mistake as 'An action or judgment that is misguided or wrong'.
If Schopenhauer is correct and if God also exists then God has made a bad call by creating life - or at least 'life as we know it' (i.e. immortality might be OK if we were in the Garden of Eden instead). In which case it doesn't matter whether God is omnipotent and omniscient or not- God would have knowingly made a bad decision, at least from our perspective or some of our perspectives.
If Schopenahuer is correct and God does not exist then nature itself is malignant, either in its origin or its consequences ('life as we know it'). There is evidence from all perspectives to support that nature is either malignant in its source or in its consequences. 'Survival of the fittest' does not necessarily mean 'Survival of the most benevolently wise'. It means survival of those who have adapted to their situation, no matter whether that situation agrees with them or not. Survival of the resourceful in some cases but survival of the deceitful or those who merely keep out of harms's way even if that is a more selfish thing to do. The person who sacrifices their life to save another person has been a victim of nature because it has cost them their life and the world has also lost a benevolent person.
I agree with Schopenhauer. On the whole, life is a great mistake. How can it be, for instance, that Shakespeare lies dead whilst those who have not an iota of his insight are alive , indeed are profitting from him? He was not a mythical, magical person from history. He was a person with feelings. Would not his immortality, or the immortality of say, a great architect, have been a great thing? But no- nature decides that a new generation must be born to be or not to be educated in a way that might be fulfilling or that might be even half as good as those experienced by some people centuries ago.
If there is a God He works in utterly messed up ways. But so do his people. So maybe if people change their ways and be far more good to each other and intelligent about each others needs, desires and abilities, nature itself will follow and we might even have a life worth having immortality in rather than one where immortality only seems desirable if you actually live in one of the more desirable places and have something worth saying or contributing for eternity.