To think dry cleaners could manage Monday morning?

Well it doesn’t work for his business

you also really need to have a spare set of shirts. Anything could delay your pickup on Monday morning. Owning 6 shirts instead of 5 is not a burden.

If they can't do it they can't do it, can't you just buy another shirt each so you have a 6th to wear Monday?

I used to work in a launderette, there was a 5 day turn around for dry cleaning.

You have absolutely no idea the workload the dry cleaners has already. They told you Monday PM as that's when they could deliver the service.

If it's that big of a deal, buy two shirts or launder 2 yourself for the Monday and take the rest. Maybe take the shirts to the dry cleaner more often so there isn't as many in one go.

Your poor planning doesn't constitute an emergency on their part. Taking something Friday and expecting it Monday is a tall order.

Yes, our nearest dry cleaner doesn't actually do anything on site, so we go to the further one that does, and they are usually able to do things pretty quickly if we need.

My husband has a lot more than a weeks worth of shirts though so its never usually a stress.

Buy an extra shirt each?

I reckon if you can afford to outsource the laundering of your shirts, you can probably buy one more each.

What do you do if one gets stained / torn, have to go out the same week to replace it?

The person ironing may well collect (a lot of items!) on Friday afternoon and drop off some time on Monday. Then he will check them. He is NU to state that timescale is not possible. YANBU to say that doesn't work for you....but you'd need to find somewhere else that can accomodate your needs

Presumably you have other laundry to wash, could you maybe do a load of shirts and then get someone to just iron them. They might have more flexible terms, and would possibly pick up and collect from your house?
(Every other MN is advised to take in ironing if they need extra money)

With all those carcinogenic chemicals in dry cleaning fluid I'd only use for a lined suit that's not directly touching my skin. Wash the shirts!

He's not your Mum!
Can you launder two more shirts over the weekend?

Just buy more shirts surely?

Usually dry cleaners manage this no problem whatsoever.

so take them to the place that offers the service you want.

He can't offer you the service you want, so you find a solution yourself, doesn't matter if you think he should be able to do it or not, he's allowed to tell you a realistic timescale and you're allowed to go elsewhere if it doesn't suit you.
Doesn't matter why he can't do it, he can't. Getting bent out of shape because you can't have what you want doesn't change that. Not everything can go your way every time.

Your problem is that you aren't taking them to a dry cleaner - you are taking them to a middle-man who will take them to a cleaner for you.
Find a different cleaning service that will do them on-site. Better still, given that shirts & blouses can be water-cleaned and don't need dry cleaning, you could book a local ironing service for every Saturday, set them off in your own washer on friday night with a timer set so that they finish at 8:00am and arrange for the ironing person to arrive at 8:00 and iron the shirts.

OR simply buy two more shirts so that you have a spare ready for Monday.

YABU.

Surely it would be more unreasonable of him to tell you he can do it, then not deliver on time? It sounds like you need to find a different dry cleaner.

Yes YABU

The concept that potentially hundreds of other people are also probably dropping things off and asking for them back first thing on Monday seems lost on you

He was upfront with you. He might have numerous others ahead in the queue. If the service isn’t good enough, you take your business elsewhere.

Am I being unreasonable?

Of course you are, you have that entitled attitude where you think a business model should change for you. If you don't like the service offered your options are to go elsewhere, do it yourself or pay someone to come round and do it.

This particular dry cleaner is telling you he can't do it in that time. It's inconsequential whether other dry cleaners can, he can't.

You either take your business elsewhere, or you buy a couple more shirts to add to the rotation (probably a smart move anyway).

It's not up to you decided, I could decide my butcher should really stock newspapers doesn't mean they will

Find a better service, one whose operating model better matches your requirements.

We have a regular (albeit fortnightly) laundry service. We fill the laundry bag they provide, which is collected from our garage next to the front door by 07:00 Mondays. Washed and ironed or just ironed and returned before noon.

We put up a rail for the shirts on hangers to be hung up in on return

I have no idea how they manage this but it's quite wonderful. Originally Had to wait a while for a slot to become available and now would give up a lot before this service.

Our laundry service does this but they are onsite and we also have 7 shirts per person incase there's an unexpected delay or incident.

Just realised you must both already have 6 shirts, given you're wearing it on Friday when 5 shirts are dropped off.

Get a 7th shirt!

It sounds like you both need a 6th shirt.

No he cleans them and sends them out to be ironed which is fairly common.
@rottingparsnip you really need an extra shirt each as you haven't left enough time or use the service that you used previously that can do them in the timescale that you require