Neutrinos are very small and interact very weakly with us. This means that the chances for them to hit an atom within our body, are very very small. Therefore, they can go right through our bodies without us feeling anything!
Most of the neutrinos that go through us come from the Sun, which emits billions of them per second towards the Earth. Again, since they interact very weakly, they can travel through space without getting stopped and therefore, they arrive to the Earth and go through us as well!
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