The categories or predicables are part of the syllogistic "logic." Which was not yet strictly a closed logic in Aristotle, but only became so with the Stoics. With Aristotle the research was still more open, and the distinction between formal rules of inference, and general reasoning about the world, was not yet arrived at in the authoritative form which it reached under the Scholastics. Aristotle was still comparable, though qualitatively different, from the Indian thinkers who took a different method and never arrived at pure formalization as did the West. The thing to keep in mind when reading Aristotle is that he's trying to snatch things out of the stream of change. So that they can become part of a true knowledge of the whole or science. Socrates is not a particular under a universal. He is a singular historical being. No Metaphysical knowledge of him is possible (only historia or historical knowledge, meaning empirical investigative knowledge). The predicables are to be distinguished from all that changes. Position relative to other things, the time in which he lived relative to events, whether he is fat or other matters which differentiate his body from other bodies and so forth are not capable to be part of a true knowledge of the whole. Aristotle aims at retrieving those feature which are unchanging. A singular is what we point at, physically. A particular, rather, is a secondary substance. It is a man as instance or occasion of the rational animal coming into being out of the eternal stock of possibilities. The structure of specific differentiation in syllogistic aims at speaking of possibilities which are not historically bound or accidental. Aristotle points towards what became, later, actus purus, the stock of all possibilities as permanently existing in the mind of God. In other words, the categories or things to be said of the beings or substances speak only of what is always, thus truly, a feature of the world. There always can be rational animals. Particular rational animals. Just as there is always the possibility of a particular triangle, which is absorbed in the principle of all triangles but must be some accidental manner of triangle. Isosceles for example.
Generally speaking there are numerous manners of understanding Aristotle resultant of the peculiar character of the questions asked, or the agendas of men in different ages. As soon as one takes an historical survey one sees that the understanding of Aristotle was not the same in the time of Thomas, for example, as in the Edwardian age, or as during the Weimar, and that it again has a general dogmatic or authoritative character in our own time under the power of the now dominant analytic philosophy departments, which is only contrasted by specific readings of Aristotle, which differ from the "text book" view now current. Thus, the student must seek a principle under which to read Aristotle, such as I attempt to give above, rather than learn by route each feature as interpreted by the general current university view which must be understood as under the spell of the authority of experimental Science which is the dark background motivation we are all born into and which did not exist in Aristotle's time, and, indeed, is of very recent origin.