Supervised Person Re-identification (ReID) suffers from severe performance degradation on unseen domains due to the domain gaps. To address this issue, we design a Domain Generalization (DG) ReID framework that is both generalizable and discriminative. In this framework, we propose a Parallel Attention-based Feature Decomposition and Recovery (PAFDR) module. PAFDR combines Batch Normalization (BN) and Instance Normalization (IN) to reduce the domain gap, but normalization inevitably removes discriminative information. We attempt to decompose identity-relevant features from the removed information and add them back to the network to enhance discrimination. However, existing methods only focus on the channel aspect and ignore spatial decomposition, leading to incomplete spatial decomposition of identity-relevant/irrelevant features. PAFDR employs parallel spatial and channel attention for a more thorough decomposition and recovery of identity-relevant features. Its parallel structure provides a regularization-like effect, improving generalization ability. Furthermore, existing loss functions use symmetric constraints, hindering thorough feature decomposition. We propose an Asymmetric identity-relevant Feature Decomposition (AIFD) loss that applies asymmetric constraints to features to match appropriate comparison objects, promoting thorough decomposition of identity-relevant/irrelevant features. Experiments show that our method outperforms existing DG ReID methods.