Complexity based explanation
Conscious life with memories and a psychological arrow, being highly complex, cannot evolve or exist in an environment at or near thermodynamic equilibrium - and a closed system not at thermodynamic equilibrium will evolve toward it. Therefore we should expect to see entropy increasing.
There is not much action in thermodynamic equilibrium - the heat death. The psychological arrow exists because of memories, and conscious observers with memories - or computers with memories, for that matter - will inevitably be well away from equilibrium. if a system is away from thermodynamic equilibrium the Boltzmann statistical argument indicates it is overwhelmingly likely to evolve back toward it.
This is exactly the sort of reasoning that crops up in anthropic explanations for the thermodynamic arrow that occur in the other main branch of the map that deals with the physics of time (note cross-relation to the equivalent node). Except that here the question is framed slightly differently. In the physics part of the map the question is: Why does entropy rise? Here the question is: Why do the psychological and thermodynamic arrows coincide. In fact they amount to the same thing since to ask why entropy rises requires a separate criterion for the forward direction of time - which we claim is the direction of memory growth.