Although it is possible to take any term X and imagine its anti-term, just by prefixing "anti-" to X, this is not the same as having a distinct opposite of every term. For one, not only are "contradictory" and "contrary" already distinctive negations, so too are there multiple senses of "contrary," and so for example:
In particle physics, a truly neutral particle is a subatomic particle that is its own antiparticle. In other words, it remains itself under the charge conjugation, which replaces particles with their corresponding antiparticles. All charges of a truly neutral particle must be equal to zero. This requires particles to not only be electrically neutral, but also requires that all of their other charges (such as the colour charge) be neutral.
That is, the scheme of antiformation is something like, "A is the antiform of B if and only if A + B ↦ 0," and this trivially holds when A and B have a zero value of the requisite nature. But then A is self-contrary without having a substantial opposite.
Or, to use the same words but splitting the hairs at a little bit of a different angle, we will often be able to distinguish between saying, "A and B are on opposite ends of a spectrum," and, "A and B are on different spectra, and these spectra are what are the primary opposites in this case."🟥 For example, the phrase "necessary evil" notwithstanding, it is not as if, in a sequence of responsibilities, the positive responsibility with the highest priority is the good, and hence the anti-evil, such that the responsibility with the lowest priority has the property of being evil, or that the property of evil-in-itself appears as that lowest priority; but the positively obligated and the negatively forbidden are on separate lists/"schedules" (the former is always to be done at some time or other; the latter is never to be done at all). —Or consider that in category theory, there is all sorts of talk of self-duality, or a certain mapping to/from some C and its a priori Copcit. (see also here).
So the resolution of the question turns on whether we are careful in differentiating general contrariety from distinctive opposition, or even various senses of the word "opposition."
🟥For example, in a seven-color spectrum 🔴🟠🟡🟢🔵🟣1🟣2 (I couldn't find a light-purple emoji), red and violet are on opposite ends of the spectrum. However, combining them does not blank out all the coloration, is not an annihilation such as when matter and antimatter collide. So, "What is the opposite of red?" is ambiguous: it has a "good" possible answer when we mean "opposition as in spectral position" but perhaps not so much when we mean "opposition as in a propensity towards annihilation."
Or consider then the symmetry question for a single geometrical point. On the one hand, per the theory of n-spheres/balls, a point sometimes counts as a 0-ball, and a perfect n-sphere/ball is always the apex of (a certain sort of) symmetry in however many n dimensions. So we might say that a point is trivially (or even "degenerately") perfectly symmetrical (modulo the relevant sorts of symmetries). However, on another abstract level, the question should not as such even arise: a point doesn't have multiple sides to compare, and we might be better off using a description like "presymmetrical" rather than "asymmetrical" (and of course not "antisymmetrical"!) for it. And then insofar as all this microscopic geometry pertains to the logical cartography of alternation/negation and contrariety/opposition anyway, we have that there is a level (or stage) of general logical representation which does not involve the having of substantive opposites: there is neither intraspectral nor transpectral contrariety, here.