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 morphisms of the Q-construction $QC$ of is supposed to something like a generalized Fredholm operator.

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

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.