Text-to-image person re-identification (TI-ReID) relies on natural-language text description to retrieve top matching individuals from a large gallery of 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 explanations 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. A new open-vocabulary, lightweight supervision, patch-phrase interaction module (PPIM) is proposed to train a standard TI-ReID model with concept-level guidance. Concept-based part phrases provide evidence that encourages the model to attend to corresponding image regions. InterPartAbility further constrains CLIP ViT self-attention to produce spatially concentrated patch activations aligned with each part-level phrase, yielding grounded explanation maps. A quantitative interpretability protocol for TI-ReID is introduced by adapting perturbation-based evaluation metrics, including counterfactual region masking that measures retrieval degradation when top-ranked explanatory regions are removed. Empirical results\footnote{Our code is included in the supplementary materials and will be made public.} on challenging benchmarks like CUHK-PEDES and ICFG-PEDES show that InterPartAbility achieves state-of-the-art (SOTA) interpretability performance under these metrics, while sustaining competitive retrieval accuracy.