Why do atoms get smaller moving left to right on a periodic table?
Atomic size across a period, in fact, has everything to do with electron shielding and the effective nuclear charge (charge felt by the electrons).

Across the period, electrons are added to the same outer level, meaning that shielding by inner electrons does not change, however, the numbers of proton increases. This results in the effective nuclear charge rising significantly (as no. protons increases while added electrons are shielding inefficiently), which of course, means that the atom has a smaller size.