according to Shinobu's (admittedly not very confident) explanations, the concept of fate exists in this world, and is ready to correct for any slight deviations from the norm. So if something is "supposed" to happen, it will generally happen one way or another even if you succeed in stopping it, for the sake of keeping the "path of fate" unchanged. If this is accurate, then the creation of paradoxes like the grandfather paradox is a legitimate issue, because it would introduce a deviation that the universe can't simply "correct for". This is similar to the reasoning that convinced Araragi that he could save Mayoi from becoming a ghost, because if he stopped her from being run over on Mother's Day and made sure she got to her mother's house, there would be no way for the universe to easily recreate those very specific circumstances again.
If all time travel to the past just creates a new branching timeline, though, then no paradoxes really exist, because there's no circular logic involved. You can kill your grandfather all you like, that'll just mean you're never born in this timeline; there's no paradox because you were still born in the timeline you came from. It's a very neat way of making time-travel work in a straightforward manner (and has the added bonus that if you screw everything up, you can always just go back to your original world, assuming the available technology allows that).