According to the Standard Model, quarks and leptons are fundamental particles (bosons are the force carriers). The Standard Model is the theory that explains the most and makes verifiable predictions, which have been repeatedly observed.

As I understand it, the particle accelerator which would have the required power to probe the substructure of a quark would need to be the size of Pluto's orbit. Needless to say, we're a long way from building anything of that scale, if ever.

In other theories, quarks and leptons are not fundamental particles. In string theory, strings are fundamental and quarks and leptons are different vibrations of the strings. The reason string theory hasn't been adopted is that it makes no predictions that can be verified which are not explained by the Standard Model.