In ancient cultures, the umbrella represented royalty and power. African royalty for instance first used umbrellas to shield themselves from the hot rays of the sun. To open one in the shade was an insult to the Sun God. The superstition about it being bad luck to open an umbrella indoors may have originated because people saw it as an act that insulted the spirits of the household by implying their protection was inadequate.
One explanation for this one comes from the days when umbrellas were used as protection from the sun; opening one inside was an insult to the sun god. Another theory: An umbrella protects you against the storms of life, so opening one in your house insults the guardian spirits of your home, causing them to leave you unprotected.