Recent advances in speech synthesis and editing have made speech spoofing increasingly challenging. However, most existing methods treat spoofing as binary classification, overlooking that diverse spoofing techniques manipulate multiple, coupled speech attributes and their semantic effects. In this paper, we introduce HoliAntiSpoof, the first audio large language model (ALLM) framework for holistic speech anti-spoofing analysis. HoliAntiSpoof reformulates spoofing analysis as a unified text generation task, enabling joint reasoning over spoofing methods, affected speech attributes, and their semantic impacts. To support semantic-level analysis, we introduce DailyTalkEdit, a new anti-spoofing benchmark that simulates realistic conversational manipulations and provides annotations of semantic influence. Extensive experiments demonstrate that HoliAntiSpoof outperforms conventional baselines across multiple settings, while preliminary results show that in-context learning further improves out-of-domain generalization. These findings indicate that ALLMs not only enhance speech spoofing detection performance but also enable interpretable analysis of spoofing behaviors and their semantic effects, pointing towards more trustworthy and explainable speech security. Data and code are publicly available.