The purpose of enforcing language laws, like all nationalist laws, is to exclude those who do not speak the language and to control the populace that does speak the language. It creates a nice controllable pond for the politicians and their friends to play in and profit from. It comes at the cost of disrupting communication with "others", of course, but those others are definitionally different and therefore - in some way - threatening or bad. It goes hand in glove with protectionism in the economic sphere. It is a form of unitarianism - that all citizens must conform to a unitary standard of speech, thought and behavior.
A liberal analysis of the issue would start from the premise that any state will contain "others"; indeed that it must. That those others - whether defined by birth, religion, caste, class, or anything else that humanity can dream up as a difference - may have different dialects, or languages, or habits, or rituals. Interfering with those others by forcing them to become a particular idea of what someone should look like and think is a bad thing; it reduces diversity and thus harms robustness.
A liberal compromise - asserting control only where needed for the benefit of all - would allow anyone to speak whatever they liked "at home", that anyone could use any language they liked in public or in education (the Kurdish problem), but that official laws, regulations, policing, etc. must be, and commerce must be able to handle, some common language. Diversity is good; intercommunication is a necessity.
Unfortunately the liberal compromise is fundamentally not emotionally nationalistic. The Catalan Insistence springs from the same deep dark pools of prejudice as does The Donald's race baiting of non-Americans. A similarity that if pointed out the the Catalan government would be ferociously denied. Indeed, as the protagonist of your story so artfully notes, the Taliban pull from the same well.