What game has made you the most frustrated?

Natural Doctrine.

Basically, an SRPG where any character death results in an instant game over. Roughly 40 minutes into a level, after completing the main objective (and moving to leave the level from where I entered, which is a thing you have to do in this terrible game), a random summoner unit spawns a creature that attacks one of my characters for very, very low damage, and then instantly dies to the counterattack...

Which gives the turn back to the summoner unit, who re-summons the exact same creature, who performs the exact same attack, which results in the exact same damage and counterattack death.

This happens over 20 twenty times. Eventually, my character dies from the minuscule chip damage, and it's game over. I walk over to my PS4, eject the disc, and snap that shit in half.

I have played some bad SRPGs in my life (I make a point of playing almost everything released in the genre), but just lol at Natural Doctrine. The best part is that you'll occasionally have folks show up in threads to explain that you weren't playing it right if you didn't like it.

Here's a hilarious screenshot:

This...fucking game...

I've studied guides, I've seen videos, I've spoken to people who have platinumed the game and I still do not understand the initiative system.
Natural Doctrine.
The best part is that you'll occasionally have folks show up in threads to explain that you weren't playing it right if you didn't like it.
It's okay to not be good in the game...

From your story, it seems the AI just chained multiple turns and killed you using a blind spot. The game does have checkpoints mid battle, IIRC, so you might have just lost a few turns.

This...fucking game...

I've studied guides, I've seen videos, I've spoken to people who have platinumed the game and I still do not understand the initiative system.
It's one of those things that suddenly "clicks" inside your head. Each attack will have a condition for giving extra turns, for example:

Guard - gives a turn to everyone in a adjacent square.

It's how you use 5-6 of those chains that makes this game a thrill. You need to attack and kill enemies as fast as possible, while carefully positioning your units to avoid being blindsided or killed by them in their turn.

EDIT: the true cheap moment of the game comes as the last stage. I managed to finish it, but oh boy, they weren't pulling any punches there.
Risen 2: Dark Waters. You had to spend absurd amounts of gold to get basic defensive features of combat. Most combat encounters boil down to cheesy tactics or mashing attack in hopes to stun lock your opponent. For me, the appeal of the game was to overcome its broken combat out of pure spiteful frustration.
Mega Man 9 is the only classic Mega Man game that has actively made me angry. Sure, 1, 2 and 10 had their bullshit moments, but Wily's Castle in MM9 was infuriating.

After losing to Wily for the fourth time (and I swear he had maybe 4 pixels of hp left) I said fuck it and deleted the game.
Really? MM9 is the only one I managed to beat. The series is pretty tough though. MM1 especially.
The most frustrated I've ever been at a game was the bugged boss in Star Wars: the Force Unleashed in the second to last level where the button prompts the game gave you were wrong (at least in the 360 version). I spent hours of anger on that garbage.
World of Warcraft.

Pre-nerf M'uru back during TBC. 440+ attempts to kill it, which was about average for the guilds that actually managed it.

I've never experienced anything remotely as intensely Bullshit than that fight.
First that comes to mind is Bloodborne.
Bought it never having played any Dark Souls games. Kept dying and ragequit after a few hours of no progress beyond the first area. To this day I still struggle with Blood Starved Beast.

Also, Mirror's Edge. The controls are so annoying.
I literally spent about 5 minutes at one point trying to get up this one bit. The character just wouldn't grab onto anything. It only took me 4 hours to get through the story but because of the terrible controls it felt much longer and I was desperately wanting it to end. I can't bring myself to play the sequel.

Had a friend ask me that today and I immediately thought of

Isn't that mission optional?

That was hard? I just tapped accelerate and had a bunch of fuel at the end.
I read somewhere that it was bugged on PS2 and made the fuel run down quicker. I hated that mission so much because of it.
I remember getting really frustrated with Jak 2 when I played it as a kid. The combination of long missions, heavy hitting enemies, and unforgiving checkpoints (read as practically nonexistent) made me give up on the game. It's really a shame too because I adored the first Jak & Daxter and still do an occasional 100% replay of it. Thankfully Jak 3 fixed some of the issues from the 2nd game from what I remember because I enjoyed it a lot more.
A little known but quite fun Namco made game for PS2 called Urban Reign. It played like Tekken Force mode, and even featured Eddy and Law as playable characters (probably what made me buy the game, or at least attracted me to it).

I lost a few times to a boss, I don't recall which, but it ended with a broken controller. I was about 17, and I regret it as it was a cheap 3rd party controller that you can no longer get but I loved. I ended up finishing the entire game, so me breaking the controller was me punishing myself for not being good enough at the boss.

Urban Reign gameplay: https://www.youtube.com/watch?v=AylIzCjLF38
For MP World of Warcraft.

Single player Sonic Unleashed. Between the need to collect medals and Werehog stages I gave up. I rarely consciously give up on a game.
Playing classic Day of Defeat on Avalanche as the Americans would very often elicit a special kind of rage on me.

Quite likely one of the most one-sided maps I've ever played.
Final Fantasy XI.
my angriest memory in gaming was when i joined a party and we went on an expedition to some far off place (i forget where) to grind on some high level enemies. took forever to get there and once we did they decided to boot me because i didn't have a sub class. then one of them had the nerve to sexually harass me as a bunch of skeletons slaughtered me and everybody just stood by watching

a lot of assholes played the game back in the day
Might actually be Splatoon for me.
Splatoon and Overwatch are pretty much only multiplayer shooters I've touched, and between those two you're way less likely to not be frustrated if you lose in Splatoon. In OW you can at least be satisfied with that one quad kill/good rez/enemy ult cancel/POTG after the round, even if you lose.
Isn't that mission optional?
With that attitude, yes.
Multiplayer: World of Tanks. I had to stop playing it before the game would drive me into alcoholism. MOBA's would probably drive me insane in no time.

Single player: Tough one... Probably Grand Theft Auto III and the god damn time limited missions. I HATE time limits.
Right now its PUBG.
Ive won solo twice, early on in my time with the game but i havent been able to take first for the last 100 hours or so. Its become such a thing for me that once im in top ten like im having palpatations. Its like a cross between rage and anxiety
Are...you me? I literally did the same thing haha. Wasn't during a losing streak, but something pissed me off reaaal bad in Overwatch and I ended up breaking my controller. I don't ever get mad like that with games but as much as I love Overwatch it can really get the salt flowing at times.
It really can, like nothing else really.
I generally don't swear much, but Overwatch has me cursing like a sailor sometimes. Getting one-shotted by Hanzo, being constantly pestered by a Tracer with a seemingly infinite teleporting rate, a Genji that's impossible to aim at due to his mobility and a team that refuses to acknowledge the payload - these things and many more just frustrate me to no end. I love and hate that game in equal measure.

I don't even play competitive anymore because I get too worked up about things.
In my youth I would have said the last bosses of a lot of fighting games. Those cheating bastards pissed me off.

Now I'd say the has brought me the most frustration ever is hearthstone. And nothing else is even close to it. It's slowly gotten a bit better but every expansion still has one to two really bullshit RNG cards that will fuck you over no matter if you're the better player