I am not familiar with Danto's work specifically, and therefore I don't know whether he was trying to distinguish between art and non-art, although I suspect that he would say that stating that a painting is not art is an oxymoron. But to me, from this quotation, he seems to be saying that there is no such thing as a meaningless work of art, and that its meanings are expressed symbolically, not literally, through the forms, shapes, colours, lines, marks, or whatever, comprising the object [we may find the Grand Canyon beautiful, but it is not a symbolic artefact; a picture of the Grand Canyon may express our feelings about it, but it does so symbolically, since is not the Grand Canyon itself, but a set of coloured splodges on a flat surface]. These meanings are entirely encapsulated within the work, often in a set of symbolic codes that may or may not be consciously placed there by the maker, and may or may not include contextual factors, but nonetheless are limited by the object, which is conceived of as a passive receiver and transmitter of these meanings. In other words, our task as critics is to unpack and interpret this finite set of meanings (implicitly including the 'invisible', or at least the obscure, or not immediately obvious, or requiring specialised knowledge to detect). Thus "criticism is just the discourse of reasons".
There are a number of objections to this approach. Some examples:
(1) Material culture theory argues that meanings are (also) embodied in the uses to which an object is put, or in the perceived purposes of the object at any one time in any culture, which may have nothing to do with the symbolic expression of its makers' ideas, or the culture that produced it; for example, the 'Mona Lisa' can be understood as a prime focus of an economically crucial international activity, tourism, and of a whole lot of other things peculiar to our time that could not have been anticipated in the early 16th century, rather more than as a portrait of a long-dead Florentine called Lisa Gioconda.
(2) The concept of 'agency' argues that the work is a receiver of meanings, but is not passive. For example, once made, it may encourage of itself the creation of other similar objects, or even classes of objects, that would not otherwise have existed; or the particular visualisation of something may have an unanticipated impact on the understanding, or misunderstanding, of a phenomenon.
And so forth.
In other words, once made, an object seems to have a life of its own, and continues to receive and transmit all sorts of meanings. So perhaps Danto is right to say we must be "ready to interpret it in terms of what and how it means", but wrong to suppose we can ever fully do so, since these meanings will continue to accrue as long as the object exists (and probably afterwards too), and wrong to suppose these meanings are entirely embodied by the object — if that is what he is arguing: to repeat, I am responding only to this question, not generally attacking a theorist whose work I have not studied!