Why do humans have parts in sets of 1, 2, 4, and 5, but not in 3?

It’s not about number. It’s about symmetry and balance.

If you had three arms, you’d be asymmetrical and fall over.

If you had two heads, there would be no center of control, and imbalance would result.

As for the number 5—yes, fingers and toes come in sets of five. But groups of fingers and toes (hands and feet, in other words) come in symmetry-ensuring sets of two.