Distance is not a social construct, but units of measurement for distance are, even though there are always objectively consistent and inconsistent ways of measuring distance. The same is true of time. Of course, the units of measurement for time are social constructs and can only be arbitrary by nature, but they are not time itself in the same way that an environment of a certain size is not the words or units used to refer to it. A unit of measurement for time would be useless if it was not actually measuring or at least intended to measure something. Moreover, someone who denies the existence of time to themselves or others must ironically do so at a given instant, so there really is such a thing as a "moment" of time--time elapses whether or not people call certain periods of time seconds, minutes, or hours.
Time exists whether or not someone is intelligent enough to avoid believing it does not. Perception of tine can involve illusion, as there is no way to prove that an amount of time that seemed like five minutes or an hour is truly as long as it seemed. Logic reveals that any human attempt to verify how much time seems to have passed will always involve relying on another kind of perception that could be false, like consensus among other people or a technological device that has supposedly been accurate. Still, if any event follows or could follow another, there must already be a duration in which those events can happen. Time is not events, units of measurement, or a "sense" of time passing. It is a duration that elapses whether or not people bother to think about it without making assumptions or misunderstanding it.
The cycle of day and night is a function of nature, and the terms and units people use to describe or measure time are constructs of language or custom. To go beyond this and say time does not exist just confuses the natural world, language, or perception for time itself, which, as abstract as the issue is, is a very obvious mistake. Perceptions are perceptions, yes, but that does not mean there is nothing but perception. What units refer to is very real. In fact, that people who deny the existence of time still use measurements of time means that they are indirectly admitting that something is really being measured, or at least an attempt has been made. If this was not the case, then the same would be true of distance and feet, yards, and miles.
To be sure, no one inevitably needs an analogy to understand the basic metaphysics of time. Truths and concepts can be understood directly without something else to compare them to. It is still true that the conceptual relationship between distance and units of distance must be true of time and units of time. Only a fool would think that the distance referred to by the word "mile" must be a social construct or an illusion of habit. Either an environment exists or it does not, but it has a specific length and width if it does. Size is not a construct of perception and would not be even if there was no such thing as an external world at all. It is the fact that time is a nonphysical thing--a fact that is not immediately obvious to someone who does not think rationalistically about time--that drives certain irrational people to deny its existence because of the self-refuting idiocy of sensory empiricism.
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