Why are hydrogen bonds associated with water (H2O), but not with methane (CH4)?
Hydrogen bonding occurs where hydrogen is bound to a strongly electronegative element, viz. F, O, or N.
As a physical scientist you should look up a table of electronegativities and note the difference in electronegativity between oxygen and hydrogen versus carbon and hydrogen.
Electronegativity is conceived to be the tendency of an atom in a bond to polarize (i.e. unequally share) electron density towards itself. The greater the difference in electronegativity between the bound atoms, the more polar the bond (i.e. the more electron density polarized towards the electronegative element).
Since oxygen is much more electronegative than carbon (it has more nuclear charge for a start), the