To me, it's mostly about being able to stand up for ourselves on a world stage - ideally through a common EU military that is strong enough to deter adversaries even without US support.
My main reason is the instability of the American political climate and the way every four years there's an election between a centrist and an extremist. Trump has already threatened to invite Putin to invade other NATO countries [0]. We can't risk being dependent on this madman.