I am working on a chemistry problem set and the answer key says all H's will show up as singlets. This does not make much sense to me as there are adjacent hydrogens to each carbon which should mean the H's show up as a doublet. What am I thinking incorrectly about this?
All four hydrogens are equivalent and therefore they do not display any coupling to each other. (They do couple, but the coupling cannot be seen in the spectrum.) See: Why don't equivalent hydrogens cause splitting in NMR? for more discussion of this topic.
Just to be extra nitpicky, I wouldn't write "all four hydrogens show up as singlets", since that implies that there are four different singlets. I'd write something like "one singlet is observed in the spectrum, corresponding to all four hydrogens".