Fashion Emergency #2d #dimensions

Can you tell what's wrong with this picture of our 2D friend? They live in a flat world where there is height and width, but no depth, which means that this hat is as illegal as wearing mismatched shoes, or as incomprehensible as wearing your cat's Christmas sweater. This portion of the hat is causing the problem. It cannot pass in front of the head because everything must lie flat on the plane. This image is an emergency because it implies that a section of the brain is missing and has been replaced by a hat. Instead, from now on, all hats will be drawn either on top of the head like this, or as is increasingly trendy like this. Backwards hats will be drawn like this or this. Now for another question. If a 2D creature wore pants, would they wear them like this or like this? I'm afraid most other options would fall off.