None of these answers quite get to the point of why a day must be the 24-hour day that corresponds to a revolution of the earth.
I can’t speak for his particular sect, but I think the answer lies in the um, evolution of the way sects have formed over time.
The List of Christian denominations page is a useful reminder that the entire history of the Church is one of splits, heresies, schisms, and re-creations.
Polycarp could give details better, but a quick broad survey would show that there were numbers of sometimes literally warring factions in the early Catholic Church over basic and divergent interpretations of the source material. (The source material, i.e., what to include as the books of the New Testament, itself wasn’t fixed for hundreds of years. Purported Gospels continued to be written, or “found” as late as, IIRC, 800 CE. List of Gospels.) It wasn’t until Constantine converted to Christianity and called the First Council of Nicea in 325 that the Catholic creed was set in place. Modern Roman Catholicism stems from this and the power of the Church in the former Roman empire kept it going as a more or less coherent body in western Europe, but Orthodox Christianity split into a separate body centered in of all places Constantinople. (Yep, he was that influential.)
When Martin Luther split off what became Protestantism as a body of understanding that did not require the intersession of a hierarchical church to interpret for you, Protestant sects immediately began to increase in number. Or without number. I doubt anybody knows how many individual sects exist. For that matter I have a standing bet that no one can tell me what all the doctrinal differences are that separate the 40 or so American Protestant churches that have more than 1,000,000 nominal adherents. (Perhaps a handful of Professors of Comparative Religion can, but not in a closed book final. :))
From the outside, all of these fine lines are distinctions without a difference. Internally, however, they are of the greatest importance. They are what define a religion and what separates that religion from all others. Without these doctrinal definitions, there would be no religion there of that name in the first place. It’s of supreme crucial importance to enumerate them and defend them at all costs.
And that’s why some sects have latched onto the definition of the day in Genesis as being 24 hours. Other sects don’t. That may seem simplistic but it’s equivalent to every other hairsplitting distinction that tore groups asunder over the last 2000 years. Your belief is not my belief. I will cast you aside because of these differences. Or I will start my own church - a trivial matter in Protestantism as opposed to Catholicism - to insure that my differences rule your belief.
None of this is exclusive to Christianity, of course. All the fatwas, rules, edicts, and proscriptions found in Islam are from hundreds and hundreds of sects that proclaim their beliefs to be supreme and want to force others to behave similarly. Christians who look to their history have no cause to complain about the similar behavior of others. They do complain, but I complain that nobody knows history these days.
As long as I’m being long-winded, another irony is that Christians, especially those of the Creationist persuasion, like to talk about science being a belief no different from religion. But even this short potted history shows otherwise. Science comes to a consensus based on the source material and then keeps it, adding that consensus to all the others to get a unitary whole that governs the behavior of all scientists as they do experiments. The consensus changes as new information is found but is always incorporated. Otherwise, no one could tell the value of a experiment’s results. This is the opposite of religion, which starts with a source of information not to be changed or added to, but each experiment - each sect living its life in a particular time and place - changes the interpretation of that source material and splits into smaller and smaller groups with mutually exclusive claims. There are no ways of looking at the universe that can be more opposite than science and religion. (Linking science and atheism also doesn’t work, since atheists have no consensus and no unity. Nor can a lack of belief equate to a belief.)
Fun as this is, the answer to the OP is that the belief that a day must be a day is important because that’s what they believe. Circular, but true.