Stars do not fall into black holes at the centers of galaxies because they typically orbit around the black hole due to the gravitational forces at play. The motion of objects, including stars, is governed by the balance between gravitational attraction and the object's momentum.
In the case of a galaxy's central black hole, such as a supermassive black hole, it has an extremely strong gravitational pull due to its immense mass. However, the stars within the galaxy also possess their own momentum and are in motion. This momentum keeps them in their orbits around the black hole, much like how planets in our solar system orbit around the Sun.
The gravitational forces from the black hole act as a centripetal force, continually pulling the stars inward, attempting to make them fall into the black hole. However, the stars also possess enough tangential velocity or orbital speed perpendicular to the gravitational force that they maintain their orbits. This balance between gravity and the star's motion prevents them from falling directly into the black hole.
It's worth noting that occasionally, stars can come close enough to a black hole to be captured by its gravitational pull and eventually fall into it. This process is known as tidal disruption, where the intense gravitational forces from the black hole stretch and tear apart the star. However, the majority of stars in a galaxy's central region remain in stable orbits around the black hole without directly falling into it.