Is there a word for this? Related to arguing with people.

[Lookingforthis]

It can happen sometimes at work when you've told someone you can't do something because it's against company policy, or it just can't be done for whatever reason. It can also happen in your personal life when you've said no to something, sometimes with a reason, and sometimes just because no is a complete sentence.

The other person will then launch into a pseudo-academic/pseudo-intellectual discussion about why they think they should be able to do that thing. It's not straightforward customer service stuff where the customer is often right (e.g. your courier lost my parcel, therefore you should send me a new one free of charge), but more academic or philosophical stuff, almost as if they've joined a debating club or something.

Does anyone know what I mean? Is there a word or phrase to describe it?

Pontificating? That's not quite it, from what you've described, but I haven't experienced what you've explained in your OP.
Hectoring, maybe?

Pontificating is a good word. It certainly puts across that the person doing it is being a twat. But I still think we need another word for it.

It's bullying, really - they're trying to manipulate the other person in to doing what they want by intimidation/blinding them with science/whatever

I bet you're right, though, and there's a word for this - following with interest!

If there isn't a word for it, we need to make one up.

Haha !! I work with a guy just like this. Hes a narcissistic tosser !!!!!

I think a lot of these people are more concerned about Being Right, rather than trying to get something tangible out of the situation.

We used to call people like that a PIA. Pain in the Arse.

They're certainly a pain in the arse! But we need a word to describe the pseudo-academic angle.

Another example would be people who try to haggle or ask for a discount at charity shops. The prices are set by the charity, maybe sometimes by the charity head office, but they'll put forward an argument that it's too expensive or that charities should be doing more to help shoppers gud bargains etc. I've actually seen a few charity shops with signs up asking people not to ask for discounts.

Not quite right but : arrogant?
They've been told no, but in their arrogance assume 1) they know better 2) you care what they think 3) you want to hear their thoughts in minute detail 4) you will see the light after they amaze you with their wonderful thoughts

Sophistry?

bombastic rehetoric
blathering
disputatious?

"Arse-wankery at degree level" is what I mutter to myself on a regular basis.

Argumentative?
I had one of these at work.
Him : what do I do about this? (Slighty out of our usual stuff question)
Me (possibly after clarifying questions) : in that case the process is X y z.
Him : I think the process should be ABC.
Me: well I can see it might not be clear cut. But because of blah blah,. The process is X y z.
Him: blethers on.
Me: I understand you don't agree with the process, but it is xyz. My team can't change it, your team can. Perhaps take it up with you regarding line manager.
I spent fucking ages explaining stuff to this person, until I realised it is basically a sport to him. The previous person working with him had all manner of strategies to avoid him. I always go back to "ask your manager'. Unless it's a bad week, then I offer to chat to the manager myself, then others are aware what a pita he is.

sententious?

Sententious - trying to appear wise, intelligent, and important, in a way that is annoying. Taken from Cambridge dictionary

I like sententious - much better than my go-to ("cunt" )

Try combining: sententious cunt.
Best of both worlds there.

Belligerent? I know exactly what you mean. In fact, teenagers do it a lot when told they can't do something.

Well, as this is MN, surely the word has to be 'entitled'

More suggestions welcome.

What about gainsay? That is contradiction of a statement

There is a military phrase ' don't fight the white'. Roughly this translates as wanting to ignore the rules/questions, as you don't like them. When ds used to give me a diatribe or a specious argument about why he shouldn't do his homework, whilst knowing he would eventually have to knuckle down and do it, we told him he was fighting the white.

The white refers to the colour of the paper on which tasks/instructions are printed.

Pedantic maybe !?

Don't think 'don't fight the white' would go down well with 50% of our students, somehow.

I'll stick to 'you're annoying me now and I'd far rather not put you down for an SLT detention if I can help it. Your move'.

it's far less likely to get me fired, for a start

I did specify it is a military phrase and that it refers to the colour of the paper upon which tasks and instructions are printed Mitzi

Why does every bloody thing have to be seen through the prism of racism? I had a blackboard when I started teaching, as its colour was black, then I got a white board. What are these referred to as now? Why would using a military phrase, which has been put into context, get you sacked?

I knew the minute I posted there would be a response like yours, hence the qualification of the phrase and its origins.