This is mildly infuriating, I can give you a little more context though if you're interested. I don't know exactly about contracts between insurance companies and CVS so I can't speak to that definitely. Probably something related to how much insurance is willing to pay minute clinic for such a short visit, and what things are feasible to address in such a short visit (hence CVS only allowing certain complaints).
I think this is something to do with the concept of "uncomplicated" vs "complicated" uti. Complicated utis are when there's an increased danger of serious complications from a uti or increased likelihood of failing a typical antibiotic therapy. Utis in men are much much rarer than women, and are considered to be an automatic "complicated" uti by many. The greater length of the urethra in men helps prevent bacteria from being able to travel up to the bladder, whereas in women the short distance allows for this to happen much more frequently. So when a male has a UTI there is a much greater chance there will be complicating factors like prostate issues, structural problems, kidney stones, kidney infection, catheter use, atypical bacteria, etc. If you look more into their info on utis, they also state if they suspect any of those things, even in women, they won't treat it and will just refer you to someone else, probably the Ed or a real urgent care clinic. Since the odds of that are much greater in men, they probably aren't allowed to have longer appointments in minute clinic based on what insurance will pay for what they're providing, they just decided to not see that at all in minute clinic. Looks like they do see men for sexually transmitted infections though, which are actually the most common cause of utis in young men, so if that's a concern looks like they would be able to see people for that.
But I totally agree with you, fuck insurance companies in general.