A bag containing food is a one-use item and is discarded after it is emptied.
Conversely, a can (such as a tin of tuna fish) is capable of being re-used and must therefore be rendered useless before opening (typically by punching a hole in the bottom) to avoid committing the melacha of makeh bepatish - finishing a utensil (literally: the final hammer blow).
Chopsticks are a reuseable utensil (even if you chose to throw them out afterwards - most people don't reuse tin cans) and separating them is a necessary step to their use. Thus, it is forbidden to separate them on shabbos.
Lastly, it would appear that separating them on Yom Tov would be permitted under the principal of "ayn bein shabbos viyom tov eleh ochel nefesh bilvad." Similarly, people who wouldn't even open plastic soda caps on shabbos will do so on yom tov, and "disabling" tin cans is not necessary.
PS: Sorry, I cannot point directly to the relevant halachic sources at the current time. I do not presently have access to my shmiras shabbos kehilchatah and mishna berura. Please feel free to edit them in if you find them.