I think this word describes what you are doing posting that cut out image very well,
Quote mining :  (also contextomy) is the fallacious tactic of taking quotes out of context in order to make to make the comments of an opponent seem more extreme or hold positions they don't in order to make their positions easier to refute or demonize.[2] It's a way of lying. This tactic is widely used among Young Earth Creationists in an attempt to discredit evolution.