This paper argues that Large Language Models (LLMs) should incorporate explicit mechanisms for human empathy. As LLMs become increasingly deployed in high-stakes human-centered settings, their success depends not only on correctness or fluency but on faithful preservation of human perspectives. Yet, current LLMs systematically fail at this requirement: even when well-aligned and policy-compliant, they often attenuate affect, misrepresent contextual salience, and rigidify relational stance in ways that distort meaning. We formalize empathy as an observable behavioral property: the capacity to model and respond to human perspectives while preserving intention, affect, and context. Under this framing, we identify four recurring mechanisms of empathic failure in contemporary LLMs--sentiment attenuation, empathic granularity mismatch, conflict avoidance, and linguistic distancing--arising as structural consequences of prevailing training and alignment practices. We further organize these failures along three dimensions: cognitive, cultural, and relational empathy, to explain their manifestation across tasks. Empirical analyses show that strong benchmark performance can mask systematic empathic distortions, motivating empathy-aware objectives, benchmarks, and training signals as first-class components of LLM development.