Why does two species that belong to the same genus, also belong the the same family?

The reason why the belong to the same family is because there are different subsections at how species are classified.

Lets say we have three groups. Insects, Sealife, and Animals.

Well, we could actually further break those down into something like

Insects - - > Ants, Bees, Beetles

Fish - - > Algae, Fish, Crabs

Animals - - > Reptiles, mammals

And we can keep going until we get more and more specific!

They belong to the same family because the family is a more broad level of classification than genus and if they are both in the genus, they have to be in the family together. Everything in a genus classification will also belong to the same family, order, class, phylum, and kingdom. Not everything in the genus will belong to the same species. The Classification system breaks down as Kingdom, Phylum, Class, Order, Family, Genus, Species. Everything in the same Phylum is in the same kingdom, everything in the same class is in the same Phylum, which is in the same Kingdom, and so on and so forth. Therefore, everything in a Genus Classification will also belong to the same Family, Order, Class, Phylum, and Kingdom. Not everything in the Genus will belong to the same Species