The Gemara in Shabbos (113a-113b) darshens that your walking on shabbos should be different than your walking during the week, hence it is assur to take large steps on shabbos. However, in the very same place (see also Berachos 43b) the Gemara says that it’s assur to take large steps during the week because it removes 1/500 of your eyesight. The exception during the week is running to a devar mitzvah, which is also the exception on Shabbos (see Berachos 6b). Now it should come out that since during the week you can’t take large steps and Shabbos has to be different than the week, on shabbos you should HAVE TO take large steps.