Over the past decade, deep learning has become the leading approach for various computer vision tasks and decision support systems. However, the opaque nature of deep learning models raises significant concerns about their fairness, reliability, and the underlying inferences they make. Many existing methods attempt to approximate the relationship between low-level input features and outcomes. However, humans tend to understand and reason based on high-level concepts rather than low-level input features. To bridge this gap, several concept-based interpretable methods have been developed. Most of these methods compute the importance of each discovered concept for a specific class. However, they often fail to provide local explanations. Additionally, these approaches typically rely on labeled concepts or learn directly from datasets, leading to the extraction of irrelevant concepts. They also tend to overlook the potential of these concepts to interpret model predictions effectively. This research proposes a two-stream model called the Cross-Attentional Fast/Slow Thinking Network (CA-SoftNet) to address these issues. The model is inspired by dual-process theory and integrates two key components: a shallow convolutional neural network (sCNN) as System-I for rapid, implicit pattern recognition and a cross-attentional concept memory network as System-II for transparent, controllable, and logical reasoning. Our evaluation across diverse datasets demonstrates the model's competitive accuracy, achieving 85.6%, 83.7%, 93.6%, and 90.3% on CUB 200-2011, Stanford Cars, ISIC 2016, and ISIC 2017, respectively. This performance outperforms existing interpretable models and is comparable to non-interpretable counterparts. Furthermore, our novel concept extraction method facilitates identifying and selecting salient concepts. These concepts are then used to generate concept-based local explanations that align with human thinking. Additionally, the model's ability to share similar concepts across distinct classes, such as in fine-grained classification, enhances its scalability for large datasets. This feature also induces human-like cognition and reasoning within the proposed framework.