Mathematicians created an 'impossible' shape that shouldn't exist

This is a fun article that examines the journey of a ladybug traveling on a weird shape in a Klein bottle-like space, but I can't make sense of its title. I don't understand why this shape shouldn't exist. What undeniable principle is it that is violated by the existence of this shape? Maybe this shape offends the sensibilities of the author? Is the shape depressed thinking of doing itself in? I just don't know how some bit of mathematics shouldn't be when it is.

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