Why do some galaxies look like they are exploding outward (a ball) and some look like they are spiraling inward (like water down a drain)?
This has always been something I noticed. Spiral arms are formed in water down a drain, tornadoes (upside down drain), hurricanes, why would large-scale galaxies be different?
They are doing neither, they are just different shapes. The shape of a galaxy isn't fixed forever. They evolve over time and can affected by interactions with other galaxies. But a spiral isn't spiraling inward and a globular isn't exploding outward. In both cases all the material is orbiting the center.