Illogical Logic
I agree with you in the literal term how logic is logical. How we perceive ourselves, life, values, actions, thoughts, and goals all come from an established language.
I also agree in the matter of, "if your own language is not logical, then it is not logic." Meaning, if your language is logical it's logic. This essentially translates to everyone having their own individual language of logic. Collectively, we now face an engulfing logic that is larger but relative to our own, Absolute Truth.
What I'm getting at is the power of perception is what we use to establish a language of logic.
A value of Belief can make something perceive to be logical.