Neutrinos from cosmic sources are incredibly rare. If you want any real chance of detecting them you need large detectors. The neutrinos from this CERN experiment are much more concentrated. That allows them to use much smaller detectors.
a quick google estimates that a human has about 100 trillion neutrinos pass through their body every second, but only about 25% chance that even a single one will interact with any atom in your body over a lifetime.
it is a detection issue, not a quantity issue.
The situation with neutrinos is exactly analogous: IceCube looks for high energy cosmic neutrinos, not low energy background neutrinos. The latter are only of interest to dark matter searches.