I don’t think you understand the definition of the word “context.”

“Taking something out of context” means looking at an event, conversation, et al., in and of itself without considering other things around it that relate to it, and in doing so drawing the wrong conclusion of what it meant.

Taking a quote from someone and changing it entirely has nothing to do with context. Misrepresenting what someone said or putting words in their mouth is not the same as being out of context.

Hence why both of you are doing it wrong.