How can a person be very sad, irritated or angry and still not show it on their face ?

I’ve had depression for years. You get good at pretending to be happy/ok and you mostly just become numb and very good at hiding things on the outside.

Same!

I'm nonbinary and spent the last 25-ish years suppressing my feelings in order to blend in at school and work. One ends up getting very good at masking themselves, wearing a "Resting Neutral Face" so often that it becomes a reflexive defense mechanism.

I finally escaped Texas a couple of years back and got started on hormone therapy, which has been amazing. My friends and relatives have all commented on how much happier I seem now, but I haven't been able to drop the mask entirely as of yet. I still have a hard time showing negative emotions. After hiding them for so long, anger and sadness are wired in like a PTSD trigger that numbs my expression before anything more than concern can show.

I suppose it isn't all that bad, having an involuntary poker face can be an advantage in social deduction games. Not even my partners can tell when I'm the imposter in Among Us. XD
This sounds familiar. For me, add masking ADHD over enthusiasm, and other factors.
/agree

After some time, you just shield yourself automatically with several layers of mental protection and you have several ready-to-use answers so everything is fine (spoiler: it’s not)

some learn it in order to survive. others learn it to control situations - you can control how you react to things, which disarms lots of aggression/bullying. its even stronger to not actually get sad or angry when its justifiable, as cooler heads more often prevail. to wear your heart on your sleeve is a luxury afforded to the safe people.

I disagree that it's a luxury. Many people, especially autistic people, simply cannot learn this skill and they can suffer for it greatly.
- i get your perspective and thank you for sharing. i posit that if their circumstances are traumatizing enough, those many people would reroute their brains to compartmentalize. its a luxury that they hadn't had to. it's not a 'skill' that is "learned" in a typical fashion. theres no school book for it.

I can't speak for everyone but I've spent my entire life masking my depression so I've gotten pretty good at masking in general. It's just practice.

Practice probably will help. If you can find a mirror while you’re in such a state, you could practice controlling your facial expressions in front of it.

That said, expressing emotion isn’t inherently bad, though I understand there may be some situations in which you don’t want to.

Wasnt allowed to be sad as a kid, can't even try to show it on my face. Not showing it is the standard.

Had the same thing for a long time. Took me years to rehabilitate myself.

Honestly the title just sounds like what it's like to be English

Haha now that I live in English speaking country, yep. Repressed bastards.
- It's in our culture; to show great emotion is unseemly and embarrassing. To quote BBC Radio Four's version of "The Secret Pilgrim" George Smiley, a spy, tells a group of trainees that the English make great spies because "You could be standing next to a man at the bus stop have a force four mental breakdown and you'd be none the wiser." We must keep a "stiff upper lip". Outbursts are for children. Has the unfortunate side effect that people don't seek help when they really need it.

Emotional self control, I guess. Not sure what control specifically over physical emotional expression would be called. I too am interested to know more, if any behavioral science people are here.

I find it easy to suppress enotional indicators, but I am not a very excitable person when I don't want to be. I just sort of compartmentalize things, and try to only give them the energy I want to. First process, then react.

EDIT: There are some exceptions. Example: I will cry at particularly emotional scenes in movies, and there's nothing I can do to stop it.

Stoicism.

Many people think Stoicism (the philosophy) means to be unemotional - it doesn't.

It means to accept that we have emotions, some that seem to "just occur" unbidden, some that are a result of our thinking, and that we can choose how we respond to those emotions.

If we allow ourselves to just be amoeba, we're then at the whim of every stimulus.

In "Your Erroneous Zones", Wayne Dyer explains how to use CBT (Cognitive Behavioral Therapy) methods to change how we respond to our emotions.

It's not a new idea - it started with (or even predates) the Stoics over 2000 years ago, with CBT being a structured method today for applying these ideas.

Another way to look at it - your inner life is for you, what you choose of that to share with others is up to you.

I know you already mentioned it, but meditation and thought-stopping techniques are genuinely good practice for making you less reactive to immediate emotions when it's inconvenient.

Otherwise? Maybe introspection to figure out where the anger is coming from and then challenging it. Often, anger is paired with a desire to control something (a person/situation), so challenging the expectation for something to happen the way you want it to happen could be a good start.

After years of staring at a CRT monitor and increased sensitivity to light, I have developed a resting bitch face that acts out mostly on particularly sunny days.

I highly don't recommend it. I loved staring at the sky.

I am highly expressive and have little filter. I think my upbringing allowed this or even encouraged it. The meta message in every movie I ever watched as a kid was “if you just look deep inside yourself and bring out the essence of what’s there, you can do / win / be anything!” I’m also male, and my family laughed a lot and yelled a lot and angered easily and forgave easily. As a result, I’m quite outspoken and some find me bombastic or overbearing.

It’s quite hard to put this genie back in the bottle once you’re an adult. If you’re like this and wondering how other people contain it, the likelihood is that they have been conditioned to contain it their entire lives. In some cases longer than that: In Chinese culture, for example, no one has is permitted to be emotionally demonstrative and this has been the norm for thousands of years. It might even have been selected for genetically over time: outspoken peasants executed, expressive daughters disowned…

I will say this though. As you grow older your vision and hearing get worse and your feelings become less sensitive. I can hold a hot object that my kids can’t even touch with one finger. Emotionally, it’s a bit the same. Reactions come slower, and are not as strong. And the muscles in the face don’t react as much, and the heart is less inclined to engage in a full flameout over something trivial. So it gets easier.

You try to cope by masking your feelings and projecting an emotion that might release yourself from this bullshit

I personally learned to play poker as a child. Controlling your reactions, good or bad, and making them unreadable was a core part of getting good at the game.

Maybe search how to do a poker face and practice those techniques?

Now I'm picturing you and your baby pals during a play date years ago, sitting around a card table, holding cards, and smoking stogies...
- I'm picturing Baby Herman now.

Working in customer service or retail helps, once you learn how to put on your happy work face, it's easier to do in other occasions.

My maths teacher is like that at school. He's always smiling even though he's angry judging by their voice and context.

You answered your own question in part. After years of practice, the thoughts I have during formal sitting meditation have spilled out into everyday life. I find it easier to let thoughts flow through me, which helps me react much less strongly in moments such as you describe. Meditation is one way to cultivate that kind of relaxation. It's not even control, but rather repetitive practice and habit.

Trying to control yourself in those situations tends to lead to uneven results, because exercising willpower like that tends to be draining and therefore very sensitive to whatever els is going on for you. If you manage to control yourself, you'll probably want to get out of the situation as soon as possible in order to recover.

I have found a couple of thoughts helpful:

This moment will pass.
That kind of reaction (what I used to/typically do) is not helping.

Repeat. Repeat. Repeat. Calmly. With subtle determination.

Of course, none of these are quick fixes.

Peace.

For me it was growing up with religious fanatic parents who taught us to interpret the "wrong" emotions as moral failings.

I don't know where you're at in your life. Maybe you do need to learn to control your emotions more. But also consider learning to accept your emotions, learn what they are telling you, and find a healthy way to process them.

And if you have people in your life who can't deal with you having emotions, you may need to evaluate that as well.

I used to have an "awkward smile" as in I couldn't help but having an ear to ear shit eating grin whenever I was uncomfortable or upset. It would then perpetuate itself when I was conscious about it and uncomfortable at the fact that I was smiling at an inappropriate time. Took some practice at keeping a poker face initially. Once you can keep a straight face in any situation it's much easier to fake an appearance. Still exhausting emotionally, faking it.

Acting classes.

You may want to look into Stoicism.