Was it ever stated that monks can’t show their psychic powers to lay people? I heard it was one of the monk rules. What sutta says monks can’t show their powers to lay people? The Buddha showed his psychic powers to many lay people so why can’t monks?
Perhaps you have confused with this rule from the Bhikkhu Patimokkha:

Should any bhikkhu report (his own) superior human state to an
unordained person, when it is factual, it is to be confessed. -
Pācittiya 8

This rule is more about attainments (e.g. jhana, stream entry etc.) rather than about psychic powers.