There's an interesting motivation in the paper by G. Segal: 

*K-homology theory and algebraic K-theory.* K-theory and operator algebras (Proc. Conf., Univ. Georgia, Athens, Ga., 1975), pp. 113–127. Lecture Notes in Math., Vol. 575, Springer, Berlin, 1977

It is well-known that the space of **Fredholm operators** gives a model for
**topological** K-theory $\Bbb Z \times BU$.  


According to Segal, if $C$ is an exact category, a morphism of the Q-construction $QC$ is akin to a Fredholm operator.


So algebraic K-theory via the Q-construction mimics topological K-theory defined via Fredholm operators.