A fallacy of quoting out of context is when someone takes a quote from someone and changes the meaning of it by taking it out of its original context. For example, let's say someone said, "Life can be tough, but it's worth fighting for". This quote might be meaningful when taken in the context of not giving up, but if it is taken out of context and used for a different purpose, like someone talking about how life is horrible, then it won't make sense. So when you quote something, always make sure you don't change the meaning by taking it out of context.