Remarkable mechanical properties of biocomposites (bone, teeth, shell, antler etc.) are usually attributed to their special design where staggered mineral platelets are embedded in a protein matrix. Because of the high aspect ratio of the platelet the soft protein deforms in the shear mode predominantly providing the linkage for the hard inclusions. Mimicking Nature one might design materials with a similar architecture. By employing a micromechanical analysis, we study in the present work the strength of a bio-inspired composite in which hard platelets are embedded in a soft matrix made of the vulcanized natural rubber. We perform simulations of uniaxial tension of the composite material based on a continuum mechanics formulation and the high-fidelity generalized method of cells. The use of the energy limiters in the constitutive model for rubber at finite strains allows us to model failure and arrive at the overall strength of the composite. We find that the overall strength of the composite depends on the deformation and failure of soft matrix in tension and shear. Moreover, we find that the strength of the composite cannot exceed the strength of the matrix. The latter observation is noteworthy because it is qualitatively different from the previous experimental results with biocomposites which show a dramatic (ten times) increase of the strength of the material as compared to the strengths of its constituents. We illustrate these analytical and numerical findings by our experiments on 3D printed composite materials.