The Rashba to Shabbos 113a writes that it is a violation of Yeshaya 58:13
וכבדתו מעשות דרכיך ממצוא חפצך ודבר דבר
You shall honor it (the Shabbos) by not doing your own ways, pursuing your own desires, or speaking of matters.
On another level, Shabbos is the 7th day of the week, corresponding to the 7th of the sefiros, Malchus. The sefira of Malchus is the faculty of actualizing the potential of the other sefiros. Malchus acts upon the other sefiros, but does not have its own input. (R' Pinkus discusses this idea at length in שבת מלכתא.) Shabbos is the gate through which the blessing that was accrued during the week enters the world, but Shabbos itself is devoid of personal requests because it is only a conduit for generating the blessings of the other 6 days.