Wearing a jersey is essential when riding a bike, but for those who are not into wearing jerseys or cycling kits, a shirt is still an acceptable option when you ride.
However, cotton shirts do not deal well with sweat, and it may slow you down.
Imagine yourself riding for hours and soaked in your sweat.
Your cotton shirt is getting heavy as you go.
That's one of the reasons why you get rashes when you ride your bike for hours.
I know that it's not a pleasant experience.