The mechanism of streamer branching remains one of the unsolved problems of low-temperature plasma physics. The understanding of this phenomenon requires very high-fidelity models that include, for instance, the kinetic description of electrons. In this paper, we use a two-dimensional particle-in-cell Monte Carlo collisional model to study the branching of anode-directed streamers propagating through short cathode-anode gap filled with atmospheric-pressure CO2 gas. We observe three key phenomena leading to the streamer branching at the considered conditions: flattening of the streamer head, the decrease of the streamer head thickness, and the generation at the streamer head of electrons having the energy larger than 50 eV. For the conditions of our studies, the non-homogeneous distribution of such energetic electrons at the streamer head is probably the primary mechanism responsible for the streamer branching.