Ben Affleck -- Sorry I Hid the Slave Owner In My Family Tree

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Ben Affleck is owning up to coercing "Finding Your Roots" producers to omit the fact one of his ancestors owned slaves -- and admits he was embarrassed by the discovery.

Affleck copped to lobbying the PBS show to hold the slavery -- which it did -- because "the very thought left a bad taste in my mouth." In the apology, posted on Facebook, he says participating in the show makes you vulnerable ... and he assumed it would not "include things you think would embarrass your family."

The cover-up only came to light when WikiLeaks posted hacked Sony emails between Ben and show execs.

Ben says he believes America's slavery history should not be swept under the rug ... and adds, "I regret my initial thoughts that the issue of slavery not be included in the story. We deserve neither credit nor blame for our ancestors."