You're right, in a pedantic sort of way. It's an easily human readable translation of machine code. But in a practical sort of way, you can program in it, thus it can be considered a "language".
You have completely missed the point. I didn't says that there is no assembly language, but that there is not a single language called "Assembly." Practically, x86 assembly language is completely different from ARM assembly language. It makes no more sense to talk about "Assembly" as a single language than to talk about "Natural Language" as a single language. Someone who speaks Mandarin cannot communicate with someone who speaks Italian just because those are both natural languages.