The umbrella was invented to block the sun, not the rain.

In fact, ancient umbrellas would be pretty worthless in the rain, since they were made out of paper. The Chinese were the first ones to figure out how to waterproof their umbrellas with wax and lacquer. 

The "umbra" in umbrella is actually Latin for "shadow", which gives you an idea of what they were originally intended for. Umbrellas became popular in the 1500s in Europe, but only for women. Men's umbrellas didn't come out until the 1700s.