Spike-timing-dependent plasticity (STDP) is considered critical to learning and memory functions in the human brain. Across various types of synapse, STDP is observed as different profiles of Hebbian and anti-Hebbian learning rules. However, the specific roles of diverse STDP profiles in memory formation still remain elusive. Here, we show that the symmetry of the learning rate profile in STDP is crucial to determining the character of stored memory. Using computer simulations, we found that an asymmetric learning rate generates flexible memory that is volatile and easily overwritten by newly appended information. Moreover, a symmetric learning rate generates stable memory that can coexist with newly appended information. In addition, by combining these two conditions, we could realize a hybrid memory type that operates in a way intermediate between stable and flexible memory. Our results demonstrate that various attributes of memory functions may originate from differences in the synaptic stability.