Soap does not make grease dissolve the way salt disappears in water.
Each soap molecule has 2 different ends: one is attracted to water, and the other is attracted to oil.
During washing, the oil-facing ends bury themselves in a greasy droplet while the water-facing ends stay outside, forming micelles.
Agitation breaks a smear into smaller droplets that remain suspended instead of sticking back to the surface.
That is why rinsing works. Soap packages grease into tiny removable bundles, then flowing water carries them away.