I googled “why do paradoxes exist,” and I saw this part of an answer on Quora:
In general, inconsistencies can exist, because we can conceive of them, and paradoxes exist because we try to match the physical world with our conceptual view of it, and we often fail.
So a paradox may simply be a mismatch between our concepts and what really is, an inability to unify our conceived notions with reality.
It seems that stating absolutes often results in paradoxes. If I were to say to myself, “Listen to no one, not even yourself,” I would be listening to myself if I did that, which means I wouldn’t be listening to no one. Or to think that you shouldn’t listen to any of your thoughts because all thoughts are stupid would mean that you are listening to a thought.
Because of their inconsistency, it might be a natural reaction to want to toss out a paradox, to think that something is wrong or inherently nonsensical about them. And if it seems that absolutes can lead to paradoxes, one might be tempted to conclude that there are no absolutes, but that in itself is an absolute.
Perhaps paradoxes are merely a side effect of our human cognition, of our limited conceptual constructs of the world, of life, of everything.