If we assume a reversible grammar, then we make two claims. The first claim is that language should be described by a single grammar (rather than a different grammar for understanding and a different grammar for production). The second claim is that this single grammar, moreover, can be used effectively both for parsing and generation.
The first claim can be motivated linguistically as follows. The primary goal of (theoretical) linguistics is to characterize languages. How such languages are used by humans (or computers) are different questions. Thus, given a language such as English, the primary goal of linguistics is to define the possible English utterances and their corresponding meanings. Thus a single language should be described by a single grammar.
The second claim, that this single grammar should moreover be (effectively) reversible, can be motivated as follows. Given that the goal of linguistics is to define the relationship between utterances and meanings, it seems that, to check a possible theory, we should be able to find out the predictions such a theory makes. That is, for a given utterance it should be possible to `know' what the possible meanings are, according to the grammar (and vice versa). Thus, for each grammar, we want to be able to compute the corresponding meaning representations for a given utterance, and to compute the corresponding utterances for a given meaning representation.