Of course that does not bother the believers. Anyone who is willing and able to disregard the blatant contradiction that an entity is either one or three - but not both - can deny the validity of any contradiction.
What did the Church Lady say? “How conveeeeenient!!”
I’ll answer on the assumption that you are referring to the Trinity here.
For many years scientists debated whether light comprised of “waves” or “particles.” In your words, does light have to be “either one or the other but not both?” A blatant contraction you say? No just the limitations of our knowledge where contradictory things seem to both hold true.
Let me try to provide a parallel explanation for Trinity that might make some sense.
Any self-conscious person has at least two aspects: the real being of self and a concept or “awareness” of self.
Suppose an “all-knowing” Being has “self-consciousness,” wouldn’t that entail that there would be at least two aspects to this Being? The Being Itself and, because the Being is all-knowing, an identical “replica” of the Being that would proceed from the Being’s self-knowledge?
So, to counter your suggestion that there is a blatant contradiction in the idea of “Trinity,” it would seem that self-consciousness requires a minimum of two “instances” of the same being, and an all-knowing consciousness would have two indistinguishable, fully realized “instances.”
I suspect that because God is more than intellectual self-knowledge, somewhere in the “nature” of God is the necessity of a third instance, but this is not clear, possibly in the
relationship between God and His proceeding “self-knowledge” (Logos).