One dictionary definition of paradox is, " a statement (or observation) that is seemingly contradictory or opposed to common sense and yet is perhaps true. "
Keep in mind that this term was coined during the day of the self bow, which didn't have arrow shelves or if they did they were very shallow. Thus, an arrow placed on the string would be pointed way to the left (for a right handed shooter). One would think that the arrow would shoot to the left, yet when shot, it would hit the target.
That's the paradox, the archer's paradox. How can an arrow that points so far off of center strike a target straight in front of the bow. And yet it does. It's a paradox. Now, of course, through high speed photography, we know it does so because, if it is spined correctly, the arrow bends around the riser when it is shot.
Nowadays, a lot of folks mistakenly apply the word paradox to mean the bending or flexing of the arrow as it passes the bow riser. That's incorrect. The arrow does not paradox around the bow. It flexes or bends around the bow when shot. The fact that it flexes around the riser explains the archer's paradox, i.e., why the arrow, which appears to be lined up off target, actually hits the target.
On a bow cut past center in which the arrow can be made to bisect the string, as in most compounds shot with a trigger, there is no archer's paradox. Of course, the arrow still flexes horizontally and vertically when shot.