To be annoyed that my employer won’t let me go part time?

No heads of dept are allowed to work less than 4 days. If there's line management responsibilities you have to be available. If you want to leave and find a job for 2 days then that's worth considering but I suspect your company knows that it's unlikely.

But they’re not heads! Heads usually need to be contacted more often than 2 days per week.

could You suggest 3 days at least and spread across the week so you have good oversight?

From 5 to 2 days is a huge drop - did you ask if 3 or 4 was an option ?

Something really doesn't add up here.

OP is currently in an FT role, and is attempting to make a case that they can do the same job just as well in 2 days, without someone else picking up extra work?

This makes no sense at all to a business. They will either realise that you, in fact, are massively overpaid or they will think you are completely unrealistic/ borderline delusional about how you would manage your time 2 days a week.

Why are you replying to posts but purposefully ignoring any comment regarding how you can do your full time job in 2 days..? Not something you want to admit to your employer!

How can you financially go from 5 days pay to 2 days pay ?

Is there another role in the business available? Or do you mean, they could have created one specially for you? Why would they do that?

if there's a role available, then how can they stop you applying for it?

As a Head of Department who is very grateful to have been able to go down to 4 days after I had my Son YAB incredibly U!!

Who will manage your team the other 3 days? If they have something urgent to ask you they’ll just need to wait until you’re back? And how do you plan to easily squeeze a 5 day job into 2 days for 2 years, but then expect the employer to happily put you back to 5 days after? Why would they?

It’s all madness.

I am sorry you are struggling but two days a week is a pretty insane ask. And it’s really a bad idea to walk into a meeting and tell your boss that you are this irrelevant that no one will notice if you just stop over half your work. How do you fill your time now?

I am a line manager of a team and I have staff who are part time or flexi time (I do flexi time myself) but no one less than 60% and the biggest drops I’ve supported are going down one day a week or flexing 4 day work weeks etc. I would struggle to justify this level of change and no one in my team is head of anything.

if you want to work 14 hours a week you cannot work at this job. I don’t know your company but where I work you couldn’t magic up a new job for someone who was struggling. I’ve also never seen a 14 hour a week job advertised but that’s not really the point.

can you take a leave of absence while you do some job hunting?

So there's the answer as to why your job can't be done as 2 days a week.
unless all the staff you line manage only work the same 2 days a week.

I would be very careful in this situation. I fear that you might be talking yourself out of a job. You say that they have told you you are brilliant, but their actions are saying otherwise. They are not trying to keep you (at least that is how it seems to me reading your responses).
Is it possible they have in any way been sweet talking you in the past trying to encourage you or smooth over difficult situations?
You sound very determined right now that they must do what you want. Not many people respond to that well. Be careful that you don’t burn any bridges.
Good luck.

And who do you suggest covers those responsibilities on the three days a week you want to take off? YABU and you haven’t thought this through.

Why on earth are they paying you for 5 days a week then?

No wonder so many employers don't want people working from home anymore, when you hear shit like this! Clearly, there are some people who swing the lead, and make a tiny amount of work that they could do in 2 days, last 5 days.

Unbelievable!

(Yes I know you don't work from home, but you doing 2 days of work in 5, is a good sign that many jobs need re-evaluating!)

How can do your full time role in 2 days including line manager responsibilities??? When would you do any work? Would also be a really poor experience for your team.

begs the question of what are actually doing for 5 days though?

What is the sickness policy like? Just thinking you might have to make use of it if it's reasonable to give yourself some breathing space. Worth contacting your GP because sometimes you need signing off for your own wellbeing whilst supporting a difficult home situation.
Could be worth joining a Union for advice and support. The company's lack of flexibility is unhelpful when they know the home situation. Despite what they say, are they trying to get rid of you?

Kindly OP- why would they do this? They don’t have to, they are a business and not your friend.

You’re not thinking straight OP. You’re adamant you want to do current role in 2 days a week. I’d be looking at making your role redundant if I’m paying full whack FTE foe someone only working 2 days a week.

why don’t you ask to WFH 3 days a week and then don’t work them if you can do your role into 2 days?

So if a role came up, you're not allowed to apply?? How?

They won't make a job for you but I can't see why they won't let you apply for a demotion if it comes up and negotiate part time hours there.
No way will you get 2 days a week as a head.

I think unfortunately you will have to suck that up and ask for 3 days. It will be extremely hard to find 2 days a week elsewhere. They may consider 3 days. Potentially you could add extra hours on and do 4 days hours in 3 days if that makes sense? They might agree to that. It isn’t what you originally asked for but I can’t blame them for saying no to 2 days x

Some suggested condensed hours across 3 days a week upthread, which might be more appealing to your employer OP. Fingers crossed

There's a reason why there aren't any 2 day per week Head of Department jobs on offer; most likely for the same reason that your request was rejected.

I thought you wanted to go from 38 hours a week to 24 or something. Wanting to drop 60% of your hours is ridiculous. Especially as you are 'Head of Department.) You need to start looking for another (part time) job @Topoftheroof

You’re not listening, you’re telling them you are taking a full time wage barely doing anything. They’ll be thinking now why they need you in the first place.