Why can I open a bag of potato Chips and not rip toilet paper?
A discussion about opening a bag of potato chips, according to various poskim, can be found on the YUTorah.org website. A related discussion by Rabbi Dovid Ostroff regarding tearing toilet paper is also available.
From the first link:
Furthermore, there may be no violation of koreya here either: the Tosefta (Shabbos 17:9), cited in the Mishnah Berurah (314:25), allows tearing the leather covering of a barrel without concern for koreya, and many understand the reason to be that even if the covering is not destroyed, it is batel (subordinate) to the barrel, and tearing the covering is therefore like the mere removing of a nut from its shell (though see Chazon Ish above and 61:2 for a different explanation). Some poskim claim that our case is comparable, and thus permit tearing the bag (see Igros Moshe, Orach Chaim 1:122, R’ Neustadt in The Weekly Halachah Discussion p.134-138, and Tikunim u-Miluim to Shemiras Shabbos ke-Hilchasah 9:11). Others (cited in Shemiras Shabbos ke-Hilchasah, ad loc. note 11) employ other factors for leniency, combining the opinions that the biblical prohibition of koreya only applies when doing so al menas litfor (in order to sew it later), that it is not koreya when the tear itself constitutes a tikkun, and that koreya is not violated when tearing one entity into two (rather than the tear separating two attached items).
If we take this first reason, we can understand why it would not apply to toilet paper. It is not batel. I'm uncertain about how it differs given the other two reasons.
You ARE allowed to rip toilet paper, but only as long as you do not rip from the perforated lines on the toilet paper. I think that the problem from ripping the paper at the perforation is that it constitutes measuring, which is a melacha. I don't know the source of this answer, it's just what I heard from a couple orthodox Rabbis.