Consider an overly simple example:
Say we want to calculate the checksum of "hi". Since h is the 8th letter of the alphabet, we'll say h=8, and similarly, i=9. So the checksum of hi is 8+9=17.
1) What if i is accidentally flipped to j, but it's balanced out by the fact that h gets flipped to g?
2) What if i gets flipped to j, but the checksum itself also gets corrupted and ends up being 18?
It seems that checksums can allow you to strongly suspect something, but not be certain. If so, why are they used if we need certainty?