If OPs question was actually legitimate and not just an excuse to get rid of armor proficiencies, the answer as to how you roleplay lack of armor proficiencies is incredibly simple.

If you don't have an armor proficiency, you don't like wearing that kind of armor. Simple.

Plenty of examples in real life. Soldiers in war removing their helmets because they don't like them. NFL players who removed protective padding unless forced to keep it by the league. Skateboarders who don't wear protection, even the most basic and important helmet. People who don't wear seat belts. People who work with tools who don't wear their safety glasses or hearing protection. Motorcyclists who don't dress for the slide. The examples go on and on of people not using protective equipment no matter how easy they are to use or how much sense they make to use. If you give that skateboarder who hates protective gear a free set of elbow pads, knee pads, gloves and helmet, they aren't going to put it on. They don't want it. If you force them to wear it (something I've never seen in a D&D game. "Wizard! Put on that plate mail or we will not let you adventure with us!") they are going to complain, focus on how it ruins things and might even lead them performing poorly even though there isn't a real reason it should. And as soon as they aren't forced, that gear is all getting tossed. Motorcyclists are a great example of that, as you can see people who stop wearing helmets the second they are someplace where they aren't forced to do so.