Typically, the term space is the total (often cubic) area a creature occupies (q.v. Space, Reach, & Threatened Area Templates on Creature Sizes and Monster Entry Format on Space/Reach). However, the feat Friendly Switch synonymizes space with a location on the battlefield. (Such locations are sometimes called squares.)
This reader recommends not taking absolutely literally the benefit of the feat Friendly Switch as then the feat becomes wholly nonfunctional: a creature never exits its space (i.e. the feat's benefit using the phrase "the space you just left" (emphasis mine)). Instead, a creature essentially is its space, space here defining how many squares a creature occupies. So that the feat's benefit makes sense, this reader recommends a house rule that changes the Friendly Switch feat's benefit to the following:
As part of your movement or as a 5-foot-step, you can move into a square occupied by an ally of your size or smaller, which displaces the ally into at least one square you just left. Your ally must be willing and able to move (e.g. not paralyzed) and able to occupy its new location on the battlefield normally (e.g. without squeezing).
This house rule will allow, for example, a wizard use this feat on her cat familiar and an ogre to use this feat on allied ogre, both of which were previously impossible even with a generous reading of the original feat's benefit.
This reader won't apologize for the feat's lack of clarity, but, to be fair, he will point out that the feat was originally published nearly a decade ago in Seeker of Secrets (2009) and has never been revisited.