First of all we spend most of the time in the air-conditioned offices. Some of them are so chilling cold that one has to wear a jacket.

Second - there are summer suits made from linen or cotton or mix. Wearing a 100% wool suit in the summer is a direct way to a heatstroke.

Third - wearing a jacket over the shirt actually helps you to preserve the body temperature if you have to walk on the street (better not!). An additional layer of air between jacket and shirt preserves your body from overheating.