We do not know. This may be a product of how the human mind has preferred to think in a logical way about this matter. The equivalent issue is our ability to express an unlimited number of questions about any subject. It seems that the human mind is not satisfied, nor can it intuitively comprehend the 'end' of any process which it feels ought to be subdivided ad infinitum. However, human deductive reasoning, what ever its origins, finds in mathematics a 'logical' system that seemingly demands that between any two numbers there exist an uncountable infinity of other numbers. The density of points between any two numbers, according to Cantor's Transfinite mathematics, an uncountable infinity. It is more than infinite. Also, there are as many points between any two numbers on a line, and there are points on a 2-dimensional plane and a 3-dimensional volumn!
For some answers to questions about the related matter of Zeno's Paradox, have a look at Question 1267, Question 520, and Question 432 for more perspectives on the nature of space and its divisibility.