To accept that the space is expanding you have to admit that the ruler, made of atoms, is invariant, i.e. it has always the same length, and no one has provided a convincing argument of this. The space expantion relies in the belief that this is a fact. If atoms are expanding at the same rate we were not able to measure any expantion. If, on the contrary, the atoms are shrinking thru time we can measure a space expantion without any de facto happening to the space. I dont know why the space is expanding except that we measure it. The matter may be contracting because the gravitoelectric fields have energy that is expanding and are sourced by the particles since matter is born and, obviously, we are not able to measure this fact in the lab. Un discussed model, out of academia, un-peer-reviewed, is 'A self-similar model of the Universe unveils the nature of dark energy'is 'A self-similar model of the Universe unveils the nature of dark energy' that does not need any Dark Energy, Inflation, etc.
Concluding: to the question 'Why does space expansion not expand matter?': if matter expanded at the same rate no one would be able to measure any variation. The measuring act is to obtain a ratio between two quantities and both the numerator or the denominator (the standard) can change to obtain a specific measured value. But the standard is based in the 'atom' properties (in the first link and in this recent one The physical basis of natural units and truly fundamental constantsThe physical basis of natural units and truly fundamental constants) that we presume invariables.
EDIT add:
Usually it is accepted that there are no effects on Solar system scale of the space expansion, but recently it was reported, i.e. measured, that the SUN-Earth distance is increasing much more than expected:
Experimental measurement of growth patterns on fossil corals: Secular variation in ancient Earth-Sun distancesExperimental measurement of growth patterns on fossil corals: Secular variation in ancient Earth-Sun distances by Weijia Zhang , 2010 (behind paywall)
Secular increase of astronomical unit from analysis of the major planet motions, and its interpretationSecular increase of astronomical unit from analysis of the major planet motions, and its interpretation by G. A. Krasinsky, 2004 (behind paywall)
The increasing distance is deduced in the presented model, as seen at eq. 35), pag 10 of the preliminary paper of 2002 (arxiv) by Alfredo Oliveira
A relativistic time variation of matter/space fits both local and cosmic dataA relativistic time variation of matter/space fits both local and cosmic data