If your employer isn’t entitled to know why you took a day off then why do you worry about it?
Does your work not provide any PTO days? No days off? No vacations? Does your work place require doctors note? For just a day absence???
Mine requires doctor note if it’s 3 days in a row (except if it’s a bereavement). If it’s less than 3 days in a row no one asks where you’ve been. I have friends at work. We tell each other what we are up to. But we aren’t required to. .
I assume you have been working for many years. How do you normally handle having to take a day off? You've never been on vacation and never got sick.? I find these questions somewhat unusual for someone with years of work experience.