Why is it hyn? It's basically a strange exception that's become a set phrase. For almost all singular nouns you can basically say it's either going to be hwn (masc.) or hon (fem.), but there are one or two phrases that break this rule.
The only other one you'll probably ever come across is when hynny "that" is used with pryd "time" (masc.) - pryd hynny "then, at that time".