And this notion is precisely one I reject. The author himself makes the distinction between art one likes and good art, though he doesn't offer an explicit metaphysical explanation and I wish to stay clear of any kind of relativism that may be implied. (My initial reading allows for competing interpretations of the article.)
For instance, if we take the example of the fine arts, we must distinguish between beauty and taste. Beauty is objective (and as a transcendental, is to be identified with the transcendentals of the good and the true). It concerns a thing's perfection in relation to some telos, some form. Taste, on the other hand, concerns one's subjective experience of pleasure experienced in the reception of a thing. This is why we can, in principle, speak of someone having poor taste or refined taste. Poor taste is undiscerning and lacking in sensitivity, even going so far as to prefer vulgarity to refinement. If beauty were a mere matter of taste, then we could not speak of good or bad taste, or of garishness and the sublime, except as a glorified way of saying "I like this, but not that; this pleases me, that does not". I do not accept this view, though it is the received and conventional view today. A shabby and nihilistic view rooted, no doubt, in our Cartesian inheritance.
Now, this doesn't automatically mean that there can be no debate about the beauty of an art piece. Indeed, the very possibility of debate presupposes a distinction between beauty and taste, between the objective and the subjective reception of a thing. What it does mean is that aesthetic judgement is, like moral discernment and logical reasoning, something that requires not just capacity, but something that must be refined and perfected. If we debate such things—the good, the true and the beautiful—we do so with a view of conforming ourselves to the truth, and in the case of beauty, our tastes with the beautiful, just as through ethics we seek to conform ourselves to the good.