There are a lot of good reasons for wearing a bicycle jersey that are often overlooked. It's a whole lot more than just a fashion statement.
One important feature of a cycling jersey is that the materials that they are made of (mostly spandex or a similar material) is designed to wick the sweat from your body to the outer surface where it is drawn away as you ride.
People often make the mistake of wearing a tee shirt to ride. The problem with a tee shirt is once it gets soaked with sweat it stays wet, and uncomfortable, seemingly, forever. If they knew just how comfortable a jersey can be they would probably never ride without wearing one..
And for cooler weather you can just switch to a long sleeved jersey.
A jersey typically has pockets in the back for snacks etc and long tails to cover you if you ride in the forward leaning position.
The long sleeve jerseys are usually worn in cooler weather so
many have a thermal or fleece lining for added warmth. The end result is
you have added warmth that doesn't restrict your movement and is much more comfortable than a jacket or sweater.
You can get them in very plain designs, if that is your preference, but there are so many styles to choose from you are probably going to find one that suits you just fine. Years ago there weren't a lot of large sizes available but now you can get them all of the way up to size 3XL so there really are jerseys for everyone.