Paradox: when two things are true though they contradict each other.

Solution: it is not a contradiction simply because contradictions are nonsense and we know neither is nonsense. The problem is our understanding.
danger: religion and ideology make paradoxes where the evidence is not good enough that both sides of it are right. Eg unlimitedly powerful God tolerating the intolerable evil and remaining good.

More examples: God makes all completely and so controls all so our evil choices area as much his as ours. Dead men stay dead but Jesus rose.  Certain cancers don't go away but Mary's did.

So – that is why we need a high standard of evidence (it is enough forget about strict proof! to avoid contradicting the truth or contracting ourselves without realising. there is no great evidence that we really have free will. big evidence is needed for a paradox. The bigger the paradox or the bigger you want to declare it then don’t cheat. Provide the case for it.

The only way you can tell a paradox from a contradiction is if one side is virtually as certain as the other and both are certain beyond reasonable doubt.

Nobody has the right to declare something a paradox.  It is up to them to be the messenger of the evidence so the evidence is what is really doing it.

Paradox is being abused as ideology without that condition.

Why do I care?

Because one dubious paradox is as good as another.  and we need a culture of consistent people.  Inconsistency is a mark of populatist thinking and ideolgoy and even well-behaaved ideologies