Text-to-image person re-identification (TI-ReID) relies on natural-language text descriptions to retrieve top matching individuals from a gallery of reference images. While recent large vision-language models (VLMs) achieve strong retrieval performance, their decisions remain largely uninterpretable. Existing interpretability approaches in TI-ReID rely solely on slot-attention to highlight attended regions, but fail to reliably bind visual regions to semantically meaningful concepts, limiting interpretation to qualitative visualizations over a restricted vocabulary. This paper introduces InterPartAbility, an interpretable TI-ReID method that performs explicit part-wise matching and enables phrase-region grounding. Unlike parameter-heavy slot-attention methods that yield only qualitative interpretability, our open-vocabulary patch-phrase interaction module (PPIM) guides a standard TI-ReID model with concept-level phrases. Concept-based part phrases provide evidence that encourages the model to attend to the corresponding local image regions. InterPartAbility further leverages CLIP ViT self-attention to produce spatially concentrated patch activations aligned with each part-level phrase, yielding grounded explanation maps. Finally, a quantitative interpretability protocol for TI-ReID is introduced that extends current perturbation-based evaluation metrics into the TI-Reid domain. This includes a counterfactual region removal that measures retrieval degradation when top-ranked explanatory regions are removed. Empirical results on three challenging benchmarks show that InterPartAbility can achieve SOTA interpretability performance under these metrics, while sustaining competitive retrieval accuracy.