Hatcher's Algebraic Topology says the following on pg. 2
Not all deformation retractions arise in this way from mapping cylinders, however. For example, the thick $\mathbf{X}$ deformation retracts to the thin $X$, which in terms retracts to the point of intersection of its two crossbars. The net result is a deformation retraction of $\mathbf{X}$ onto a point, during which certain pairs of points follow paths that merge before reaching their final destination.
I don't understand this. Why can't the two cross bars retract to the point of intersection without any two paths crossing?