My arguments have had far fewer holes in them than those arguing for an anti-clock, actually.
Your point about something useless being the opposite of something useful does not mean that all useful things actually have something that is the opposite of them. In fact, almost none of them do. Only a very small range of objects/ideas/concepts actually have an opposite. You have yet to prove that there is anything that could be the opposite of a clock (even with a narrower definition of what a clock is). Just saying that it is theoretically possible is not any sort of valid logical argument. Furthermore, by your definition, any useless object could be the opposite of any useful object. But, opposites are by definition unique. They are 180 degrees apart (and they have to be able to be compared to each other for any sort of opposite to be able to make sense). You can not have 2 objects that are opposite, and hten have a 3rd object that is opposite to one of them. Useless A is the opposite of Useful B. But, it would also be the opposite of Useful C, as useful is the opposite of useless (going along with your reasoning, ofc). So, are Useful B and Useful C the same thing? Probably not.
You can not isolate one trait of an object and find something that appears opposite to that trait, and then say that that object is the opposite of the first object. Is a black horse the opposite of a white horse? Hardly. Black is the opposite color of white (one being no visible light, the other being all wavelengths of visibile light (which is a highly artificial definition that only makes sense with our extremely limited perception of reality)). But, the black horse and the white horse are still both horses. They are still the same objects, just with very slightly differing DNA, resulting in different pigmentation. So what would be an opposite to a black horse? Or a white horse, for that matter? Such an object would have to be the opposite of a horse itself. Is a pony (very small horse) the opposite of a Clydesdale (very big horse) just because they have opposing sizes? Not at all.