Ah, happens all the time. Some times you need to place the plate above the container's opening and slam both container and the plate into a hard, even surface to force the pudding out. Most times you'll end up with 'fuck it' and slurp them directly.
You know... aren't most of these "puddings" actually flans?
TL;DR - Flan (and pudding) mean different things in different places.
While I suspect that in American English 'pudding' refers to something specific (I don't really know for sure), by definition it covers basically all thickened-milk based desserts. Except in British English, where it also refers to a dish of ingredients smooshed together and set in some way, such as the ubiquitous Christmas Pudding. And also to refer to the dessert course in general.
Similarly, a 'flan' does not mean the same thing in the US and Britain, with it being used in British English for things like quiche lorraine and custard tarts; the Japanese 'purin' is a very much a crème caramel, which I think is what US English refers to as 'flan'. Which makes me take a double take if you call it a 'flan', because this here is very much not a flan at all to me.
Japanese 'purin' is usually translated as pudding for convenience, but Japanese does use プディング for puddings in general, so if you really needed to be specific 'purin', 'Japanese Pudding' or something similar could suffice.
'it’s time to give up and admit everything in the UK is pudding. The sky is pudding. The people are pudding. They drive their puddings to work at the pudding where they earn 11 puddings a pudding. Sometimes it puddings pudding on pudding and the pudding puddings, but that’s okay, pudding doesn’t mind because pudding p͙͉u̘͓̭̻̖͍͍d̹̕d͕̠͉̩i͚̳͕ṇ̨̟͍̗̤̺g̡ p̱̞̙̰̪ù̷̢̱̺ḏ͍̗̭d̪̯̹̻͇̻͘͢i̳̪̗͍n̥͈̠͚̗͠g̪̞̫͖̲̰͕̹̀͢ͅ p̦̙̪͖͍̦̩̰̪̣̦̣̀͘͟ù̷͈̤̼̠͙͍͕̙̯̖̘̦͡d̷͠҉̣͓̺̮̰̺̣̹̠̯͔̀͡ͅd̢̨̞̮̙͍̤̗̲̩͚̼̝̯̕i̸̳͇̹̠̯͚̹̱̫͔̻̭͢͞ͅn̷͚̼̩͈͙͚͇͡ģ̷̫͎̗̹̘͕͎́́̕ '
This is a brand of pudding called 'Pucchin Pudding', which requires one to snap the plastic bar to let air in from the top of the container, so the pudding can slide from the container.
Similarly, a 'flan' does not mean the same thing in the US and Britain, with it being used in British English for things like quiche lorraine and custard tarts; the Japanese 'purin' is a very much a crème caramel, which I think is what US English refers to as 'flan'. Which makes me take a double take if you call it a 'flan', because this here is very much not a flan at all to me.
Pretty sure our flans are what you call creme caramel, because they are always topped with caramel. Always listed on restaurant menus over here as flan.