Why does the AraC arabinose sensing system only respond to the presence of L-arabinose?
Your question is really about the origin of specificity in molecular recognition.

The simple answer to this is that two molecules (like the AraC protein and arabinose) bind to each other because they make favorable interactions with each other. ("Favorable" here means that free energy is released in the "reaction" of going from separate molecules to the complex.) There's a number of different types of interactions, but the ones you typically talk about with non-covalent protein binding are van der Waals,  hydrogen bonding, and electrostatics.

The reason AraC binds to arabinose is that it has functional groups in the binding pockets which exactly match three dimensional organization of corresponding atoms in the arabinose molecule (see the experimental structure of the AraC/arabinose complex). You can see a schematic representation of these interactions here.

The thing about these interactions is that they only happen if the three dimensional geometry matches up -- we might write molecules in a 2D schematic form, but molecules are intrinsically 3D. So when you have the hydrogen bond between, for example, Tyr82 and the C4 hydroxyl of arabinose, it can only form that favorable interaction if the C4 hydroxyl ends up in the correct 3D position. 

If instead of L-arabinose you have D-arabinose (or L-ribose), then you have a different spatial orientation of atoms. Your C4 hydroxyl no longer goes "down", but instead goes "up". Since Tyr82 is still in the same place, it can no longer form a favorable hydrogen bond to the C4 hydroxyl - the distance is too far. There's no way to put the 3D structure of D-arabinose into the binding pocket of AraC and keep all the interactions. If you lose enough of these interactions (and sometimes one is enough), the total energy of binding is no longer favorable, and there's no driving force for binding.

Keep in mind that it's not always an all-or-nothing thing. It all depends on which interactions are destroyed by changing the chemical structure of the ligand. For example, AraC has no difficulty binding D-fucose. The difference between L-arabinose and D-fucose is just an addition of a C6 methyl group. For AraC this addition doesn't disturb the existing interactions enough to significantly perturb them. Therefore, you still get a favorable energy of interaction when the AraC binds to fucose.