imagine if the sides of our jaws were disconnected in the middle and indenpentently movable, we had no palates, and one side only had molars and the other only had incisors, and we had to use our hands and tongue to get food into the throat.

i can only assume lobsters look at us and feel equally uneasy about how we work.

Had to read this three times before I understood that they weren't trying to imply that lobsters use their varied claws to break open different types of teeth. I was very confused as to what the intended joke was.

A lot of decapods* exhibit heterochely (the claws are formally "chelae" and the legs ("pereopods") that bear them "chelipeds"). Handedness isn't even necessarily consistent within the same species.

There's a popular focus on heterochely arising because of different food types, but there are nuances. For example, this is often quite different between males and females.

In addition to just being different in size (allometry), they're often also different morphologically (in shape). For example, for crabs who prey on bivalves, one claw's shape may be more suited to crushing and the other's more suited to handling, rapid movement, cutting, etc. So it's not just about how big they are as described in the OP.

There's often also a major element of sexual selection (Mr. Krabs wasn't lying), and other major uses of claws depending on species are competition (getting into fights) and burrowing.

Etc.

* Lobsters (infraorder Astacidea, family Nephropidae) are decapods (phylum Arthropoda, subphylum Crustacea, class Malacostraca, order Decapoda) ("ten-footed").

That was the only real answer.