BOTH POSITIVE AND NEGATIVE: In speaking of antitheses we almost invariably put the positive attribute first and the negative one second, as the following short list should serve to confirm: good and bad, truth and illusion, pleasure and pain, happiness and sadness, life and death, light and dark, love and hate, day and night, heaven and hell, man and woman, boy and girl, rich and poor, beautiful and ugly, high and low, yes and no, etc. To say that man's nature is good would hardly constitute the truth; for in order to have any goodness at all he must have sufficient evil from which to create it, he must have one tendency balanced by another.
Granted that man is neither good nor evil but both good and evil (which should not be confounded with a combination of each), one can nevertheless assert that the positivity of goodness generally leads him to aspire towards the Good rather than towards its opposite which, being negative, can only take second place, as it were, to the 'leading string'. Thus, as an inherently positive phenomenon, life is geared towards goodness, but to a goodness which can only be maintained with the aid of evil.
Yes, Gide was right to contend that man was born for happiness, in that man's strongest predilection is to aspire towards the positivity of happiness rather than towards the negativity of sadness. Admittedly, this happiness ultimately depends upon the intermittent prevalence of sadness. But sadness can never become the 'leading string', or man's principal objective. For the essential positivity of our being does not induce us to pine for sadness when we are happy but, on the contrary, to immerse ourselves in happiness as if it were a natural condition, as if we had found our spiritual home. And this same positivity eventually goads us out of our sadness by causing us to pine for happiness.
Now according to Schopenhauer - who is virtually antithetical to Gide - happiness is merely the absence of pain and thus a negative thing, whereas pain itself he saw as very positive, a thing upon which life mostly depends. To follow Schopenhauer's reasoning here isn't particularly easy, but it should be fairly apparent to most people that he was somewhat mistaken. For as the accepted antithesis to pleasure, not happiness, pain is really anything but a positive thing, since we aren't driven by our essential being to pain but to pleasure, so pleasure must be the positive attribute and pain the negative one. Not being content to muddle these antitheses, however, Schopenhauer also saw fit to reverse their qualities and thus invest pain with a positive attribute - a thing hardly guaranteed to enlighten one or advance truth in this respect!
So do I therefore advise people against reading Schopenhauer? No, I don't, since there is much value to be gleaned from a serious perusal of his major works, including The World as Will and Representation. What I do advise people against, however, is being put off philosophers like Schopenhauer on account of their logical fallacies. There is not a philosopher on earth who could escape criticism for one reason or another, since there isn't one whose integrity as a human being exempts him from error. Where one believes the contrary, it can be assumed that one has been deceived by the mistaken assertions of the philosopher concerned without in the least suspecting the fact. No man is born to tell the whole truth and nothing but the truth. Yet no man is born subject to nothing but illusions, either!
A man who is prepared to give his favourite philosopher's principal target of abuse (Hegel in the case of Schopenhauer) a fair hearing or reading would strike this philosopher as more enlightened than one whose willingness to do so has been severely compromised, if not completely negated, by too slavish an adherence to him.