Earthquakes induced by the human-made injection or extraction of fluids have recently become a major concern in energy technologies. When frictional and hydromechanical conditions lead to fault reactivation, unstable slip can occur and rupture propagates across the fault with a pattern analogous to two crack tips, spreading away from the hypocenter. During the earthquake the rupture tips can propagate symmetrically or along a preferred direction. These propagation patterns are related with the effects of the earthquake, and are essential due to the predominance of almost-unilateral ruptures in large earthquakes catalogs. We study how poroelastic coupling controls the directivity of the rupture in earthquakes induced by pore pressure changes. The directivity patterns observed in earthquakes ruptures may be explained by a contrast in material properties across the fault as previous studies have shown. Here we show that rupture asymmetries may be also promoted by the pressure and stress changes induced by fluid injection prior to rupture, together with the undrained pressure response during coseismic slip. We employ fully coupled hydromechanical simulations of poroelastic media with rate-and-state faults, and analytical solutions to perform a dimensionless analysis. We observe that, depending on the flow conditions and the initial fault stress state, directivity patterns range from almost-symmetric to almost-unilateral. We explain the rupture directivity pattern in terms of the conditions of fault confinement and pore pressure diffusion, and identify two mechanisms that control the symmetry of the earthquake rupture. Firstly, the pore pressure distribution prior to earthquake, which depends on the distance between the injection well and the fault, controls the heterogeneity of fault strength along the fault. Secondly, the undrained effect due to coseismic fault slip, which is directly related to the initial confinement, causes an increase or decrease of pore pressure on either side of the fault. Our results contribute to understand the impact of poroelasticity on rupture directivity in injection-induced earthquakes and offer a feasible explanation of almost-unilateral rupture patterns.