Consider a scenario where almost half of a pixel (but not the center of it) is covered by some diagonal black object that's in front of a white object.
If you ray trace and shoot one ray in the center of the pixel then it will hit the white object, and no matter how many rays you spawn from that intersection point the part of the black object that's covering part of the pixel won't actually contribute to the final image. So with this technique the final pixel will be white.
With path tracing you shoot many initial rays at random sub-pixel positions, most miss the black object and hit the white one, but some hit the black one instead. So with this technique the final pixel will be gray, a mixture of the two objects' colors and therefore anti-aliased.
If you ray trace and shoot one ray in the center of the pixel then it will hit the white object, and no matter how many rays you spawn from that intersection point the part of the black object that's covering part of the pixel won't actually contribute to the final image. So with this technique the final pixel will be white.
With path tracing you shoot many initial rays at random sub-pixel positions, most miss the black object and hit the white one, but some hit the black one instead. So with this technique the final pixel will be gray, a mixture of the two objects' colors and therefore anti-aliased.