Ochem 2 question about Multiplicity in NMR

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The way my textbook shows the example of 1,2-dichloroethane saying that all the protons are equivalent, so no splitting occurs. However, the next statement, they say geminal and vicinal protons split. Why does that not happen in the example? Someone from class said it's because the compound was symmetric, but the geminal skeleton they showed could easily be symmetric as well.