I sold a rental home in 2018. Why is the 9 years of depreciation expense subtracted from the cost basis of our purchase, significantly increasing the capital gain?

The IRS requires it. When depreciation is taken on a business property, it must be recaptured at the time of sale.

Basis adjustment for depreciation allowed or allowable. You must reduce the basis of property by the depreciation allowed or allowable, whichever is greater. Depreciation allowed is depreciation you actually deducted (from which you received a tax benefit). Pub 946

as a wise man once said. "Never sell".

A wiser man said "Buy low and sell high!"