Many students who IF, not ACIF ==> not PAD. C: many students who want to PAD, not ACIF ==> not PAD.
On the LSAT, always translate "many" as "some." In other words, "many" does NOT mean "more." So here we can say there are SOME students with an IF, and SOME who want to PAD. But what's to say that those aren't two completely separate groups? So we know we're looking for an answer choice that involves two groups that could be mutually exclusive.
(B) does just that. To diagram:
WSIBS ==> SFG Not SFG ==> not WSIBS
Some horses who are SF ==> not SFG ==> not WSIBS
C: Some WS horses ==> not SFG ==> not WSIBS
Again, the group "Some horses who are SF" and "Some WS horses" might totally exclude arch other, so we see the same flawed reasoning here. That's why (B) is correct. I hope that helps!