Multistage, multicluster hydraulic fracturing is a widespread method used in the petroleum industry to enhance the hydrocarbon production of low-permeability unconventional reservoirs. The core for fracturing-treatment success is achieving the simultaneous propagation of multiple closely spaced hydraulic fractures to enlarge the fracture surface. To better understand this coupled elasto-hydrodynamics mechanics, a 2D model comprising a combination of a displacement discontinuity method for elasticity and a finite volume method for lubrication is presented in this paper. Furthermore, a universal tip asymptotic solution, reflecting the unique multiscale tip behavior for fluid-driven fractures, is adopted as a propagation criterion to locate the fracture front. Numerical examples are fully implemented to investigate the competition in the growth of two closely spaced fluid-driven fractures at different initial lengths. Parametric studies reveal that the competition between simultaneous and single fracture growth is governed by dimensionless toughness, which represents the energy ratio of fracture-surface creation to fluid viscous dissipation. The simultaneous growth will be promoted when the fluid viscous dissipation is dominant, while, with increasing rock toughness, the tendency for single-fracture growth will increase correspondingly. Numerical results also demonstrate that initial fracture geometric settings play an important role in this competition. A large initial length offset between two fractures will generate preferential growth for the longer fracture, even in the viscosity-dominated regime. Furthermore, this paper provides dimensionless parameters characterizing fracture deflection caused by fracture interaction. The paper concludes by identifying the controlling parameters and their field applications, emphasizing that high injection rate, high fluid viscosity, and small initial fracture-size offset are beneficial to promoting the simultaneous growth at early time, which is important in enhancing reservoir permeability.