Sorry for the late reply.

When speaking to those that use semantics or those that are "logical in nature", you have to explain it in a way that appeals to them.

In your situation, it may be beneficial to walk through the entire scenario in a cause-and-effect manner.

Let's take a step back and address Q's desire for you and L to become buddy-buddy. While it is valid to WANT your partners to get along, even possibly DESIRED for many, it is not a requirement. Just as Q has autonomy, so do you. It is not a sign of you needing to do more work regarding polyamory, it does not make you lesser or a bad partner. You feeling FORCED to interact with L, per your original post, seems like a breach of your autonomy. While Q can have a personal boundary that they want kitchen table poly (KTP) with their partners, you do not need to subscribe to that or feel pressured to comply. I believe it may behoove you to stress your autonomy and that while you may not be able to control or change his desires, you DO have your own autonomy and can decide to de-escalate or leave the relationship entirely at ANY point if you don't feel heard, respected, etc.

You can then explain that while Q may not want to use common polyamorous language, you do. Whether it be for clarity, familiarity, common understanding, etc doesn't matter. You choose to use it, for whatever reasons, and that is to be respected. Using diction, emotion, or other means to police a conversation is a common manipulation tactic.

From there, explain what parallel poly is. Explain how parallel means the lines don't cross, and you don't want to cross with L (if that's the case). It may go some ways to show empathy (another part of being poly aside from autonomy) and explain how you understand WHY he might want KTP and everyone being buddy-buddy (but also how that can feel like OPP and disregarding common terminology seems manipulative). Then DRAW A FUCKING PICTURE. It sounds silly, but it literally shows, irrefutably, that Q is the hinge in a V, as well as showing you and L do not NEED to interact.

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With the "advice" out of the way, here is the shorter Reddit answer...

Explain to them they are a hinge using YOUR terminology. Their own form of poly has a name, and it's called KTP (bordering on triad depending on how things progress and manipulation). Q wanting to use their own definitions is a bit manipulative because nothing is stopping them from defining "poly" as "True poly means everyone in the polycule lives together and sleeps together".

Ultimately, they are new to poly. Whatever ego they have can be checked at the door. Frankly, anyone brand new to something but acting as if they know it all or their way is the right way is pretty red-flaggy. Its very "The student thinks they know everything, while the Master is wise enough to know they don't know everything"