dnd 5e – Does Multi-Classing in Fighter Give You High Armor Skills?

They miss nothing. Multiclassing in Hunter provides only light and medium armor skills (as well as shields and plain weapons and combat weapons). You would have to take that too Heavily armored A trick to gain serious armor skills.

Strangely enough, cleric multiclassing provides only light and medium armor plus shields, but you also have full access to the Cleric domains, some of which impart heavy armor skills. It does not seem quite Nice that fighters do not understand that, but there it is.

Perhaps on the first level the fighter was considered too attractive for a "dip" with fighting style and second wind and very attractive additional features in second and third place. But that's just speculation. Whatever the reason, if you want strong armor from a fighter (or paladin), you must call this your first class.