To dig trenches for defense, or to firmly establish something so it's hard to change or remove.
From en- (in) + trench (ditch), literally 'to put in a trench.' Military usage dates to the 1600s when soldiers dug fortified ditches; the metaphorical meaning developed to describe deeply rooted ideas or positions.
Entrenched positions are like zombie ideas—they keep shambling forward even when evidence says they should die, because once you've invested time defending them, your brain literally resists changing your mind for biological reasons!
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