Particularly for atheists and agnostics, mathematics and science is their god. One of the lies of physics/mathematics that gives science a mystical feel to it, is the lie that the "infinite" exists in nature. They imply that by teaching that space can be infinitely divided. They also present the absurdity that the basic "point" in geometry has no size, but when put side-by-side will add to a distance. They keep this up, giving the feel that there is an unlimited world at our fingertips. This charade is probably the result of an unintentional bias caused by the fact that man has a spiritual soul and needs the infinite....the "infinite" is only an attribute of God, not the material world. The truth is, there is a smallest possible size, which entails that "analog" does not exist in nature. I believe it was Max Planck who started to get rid of the infinite from mathematics. Wikipedia makes this comment about Planck units: "Planck units may sometimes be semi-humorously referred to by physicists as "God's units"."

We can all do an easy and instant experiment at home which proves with metaphysical certitude that space cannot be infinitely divided, even though mathematics hypothetically shows that numbers can.

This can be viewed as another version of Zeno's Paradox, the physical version of it. Aristotle dealt with the Arrow Paradox, a variant of Zeno's Paradox: "If you throw an arrow, since it is motionless in any instant, it never moves". The paradox is solved by Aristotle and Saint Thomas Aquinas who both commented that time is not made up of instants and magnitude is not made up of points. (Physica, Lib VI, Pars 9; Commentaria in Physica, Lib VI, 861.) Actually, a line is an infinite set of points,

Or think in this way. If points have dimension, then (1) either if there is no other coordinate within a point, then if you put it on a line (so that it can represent a number), there must be some numbers cannot be found on that line, and this applies to plane, cube, etc (2) or if it encompasses a range of coordinates, then you can infinitely apply the same principle to all coordinates as "starting points" and then you will get sets of coordinates after sets of coordinates.

For your objection/assertion that space cannot be infinitely divided, I am not sure what to say. But a line, plane, cube, etc are abstract, mathematical objects, with their locations represented by numbers in the form of coordinates, and they are not physical. For two points A and B on line CD, as long as they are not geometrically identical, there always exists a positive real number E is such that |A-B|>E, until they become one, identical point. And I believe this applies to physical space.

For infinity, you have to sub-distinguish. There is partial infinity (partially infinite) and absolute infinity (absolutely infinite). God has the attribute of absolute infinity, and only He has such attribute. However, other objects can have partial infinity. For instance, our souls have infinity of duration/time, for the souls are immortal. Similarly, space or universe can also be infinite, for it is within God and God is infinite regarding externality (though I am not sure if space is/can be infinite, since I have no advanced Physics training).