Actually the tailor AND the military answer are both right. It depends on context.
What Does Dress Right Or Dress Left Mean?
Dress right or dress left are the phrases that are used in military or even musical context. Dress right could mean act right in a particular situation or organization. In military context, the phrase 'dress right' is used as 'dress to the right' and the phrase 'dress left' is used as 'dress to the left'. One of the phrases, similar to these two is dress to the centre. All these phrases are related to one's action.
Dress is a word that generally means to cover has a reflexive use in Old English. It is used to convey that one should direct one's steps or address one's self. In formal address, dress means to make straight or raise or set up, prepare or arrange or direct. Thus, to dress right / left means to arrange or align oneself in exact position or line with the soldier (or partner, in dance rehearsal) on your right / left.
Dress is a word that generally means to cover has a reflexive use in Old English. It is used to convey that one should direct one's steps or address one's self. In formal address, dress means to make straight or raise or set up, prepare or arrange or direct. Thus, to dress right / left means to arrange or align oneself in exact position or line with the soldier (or partner, in dance rehearsal) on your right / left.
In the Military, Dress Right Dress means to adjust yourself in formation to cover straight to the man in front of you and the man to your right. Dress left dress means the same, only it directs to the left. Dress Right/Left Dress are also used in "cover" context. Where the person can say "COVER!" whichs means get into proper alignment, or "COVER IN ALIGNMENT!". They means the same, cover can also mean stop adjusting and stand still at attention. Hope that helped