I'm relaying this question from my son...
Tearing is a melacha. But, as far as I understand, one may tear open a food bag (like a bag of chips) on Shabbat. Yet, one may not cut between the letters that are on a cake on Shabbat, because that's considered erasing.
Why is tearing allowed but "erasing" not allowed?
I'm not limiting my question to these two comparisons. There are probably others, but I can't think of them.
I used to hear about tearing for food on Shabbos too many years ago. I once heard Rav Yisra=oel Reisman in his Navi shiur say that people are mistaken when they say that "you can tear on shabbos for food". He said that on Yom Tov we have ochel nefesh but on Shabbos he has no idea when such an erroneous popular idea came from.
I too was under the impression that there are extra leniencies on shabbat which are granted because of the concept of עונג שבת. However, I was unable to turn up any source for this. In every respect, the laws of shabbat would apply equally to food and non-food items, and as others have pointed out, your example of tearing the bag would apply equally to a bag not containing food needed for shabbat (say, the pieces of a board game).
Incidentally, I remembered learning that the three conditions under which בורר is permitted are the acronym אכ"ל, ochel - אוכל, ביד (ולא בכלי), לאלתר. That is, it must be for food, done by hand and not with a specialised utensil, and done immediately prior to consumption. But in fact the אוכל in that phrase refers to taking the אוכל - good - from the פסולת - bad, and not the other way around. It would apply equally to non-food בורר (say, taking a fork from mixed cutlery for immediate use), but אוכל is just used as the most common example of sorting.
(In fact, some poskim hold that בורר only applies to food.)
You are not allowed to do the Melacha of Korayah (tearing) on Shabbos for food. Or any other melocha either.
Chazal say you are allowed to cut open palm-weave baskets on Shabbos. These were disposable containers made of palm leaves, which were only used to ripen dates. Most Poskim explain that since this kli (vessel) had no intrinsic value it was considered batel (subservient) to its contents – the food inside, and thus one was permitted to cut it the same way you may break or tear the peel or shell of a fruit or nut.
All Poskim agree that breaking a worthless peal or shell-like container is not considered the melocha of tearing. This principle extends to sugar or drinks in cartons, as well as plastic bags and the thin foil covers on top of yogurt or another such packing that will be destroyed and thrown out.
There are many questions in the Poskim as to practical applications of this principle so ask your LOR but one thing is clear:
You may not do melacha for food on Shabbos. Some types of opening and simultaneously destroying packaging is not a melacha to begin with.
