Why do resistors have tolerance?

Machines capable of manufacturing exactly the same component time after time,
with exactly the resistance you want, would be very expensive, and so would the
products they turn out.  A resistor would cost a dollar instead of a few pennies.
The machine itself, and its output, work within tolerances.

The cheapest mass-produced resistors are guaranteed to be within 20% above
or below the resistance marked on them.  And you know what ?  For most bench-
work and prototyping, that's usually close enough.