In special theory of relativity, why is 4-velocity defined as:

$$ u^\mu = \frac{dx^\mu}{d\tau} $$

and not as $$ u^\mu = \frac{dx^\mu}{dt} $$

where ${\tau}$ is proper-time and t is time in some other observers' frame of reference. What does derivation with respect to invariant (like proper-time here) have to do with contravariant components of the vector? I'd prefer intuitive explanation rather than strict mathematical.