It is a bastardisation of the law of cause and effect.
Every effect has a cause and every cause is an effect.

However using the word reason as a simile for "cause" can be easily equivocated by confusing the various meaning of "reason".

Everything has a cause, but that cause may not necessarily be reasonable or have any reason other than it being the effect of something else.

Yes, it is paradoxical.

That's an excellent question and you're right -- it's the wrong question to even be asking.

Everything in what we regard as a normal regime of time is at the end of some causal chain and in that sense for us everything has at least a proximal cause. But that's not the same thing as a "reason".

A "reason" has to be someone's thinking or plan, and that requires an agency. So the very question implies a reasoner with power over reality, and this generally leads back to some sort of asserted deity.

I think people sense that life is largely nondeterministic and they think that if they can find some Man Behind the Curtain they can persuade or influence him to act more responsibly and comprehensibly. They don't like the flaky connection between effort / intention and outcomes and want to tip some imagined scale in their favor.

It's an understandable but doomed enterprise.