Why do Muslim women think they only way to dress "modestly" is by covering their entire body with fabric?

They don't think that... it's partially dictated in the Koran (although not very specifically) and is enforced in some Muslim countries with varying degrees of covering needed... it's essentially a patriarchal construct to help men maintain a dominant position, as Islam seems to be inherently chauvinistic (although many other religions are, as well, including Catholicism)