Simple Summary: Horses respond to threats by moving away or, if that is not an option, by behaving in ways that deter the threat or move it away. These responses that help to reduce the threat are regularly labelled aggression, but this overlooks the motivation that underpins the responses which are often simply forms of defence. A catch-all term that avoids the need to interpret the motivation for defence and aggression responses is agonistic behaviour. In domestic horses, all such responses are important because they can be dangerous for both horses and personnel; they can prompt humans to defend themselves and can compromise the relationships that horses have with their carers. This study used an online questionnaire to ask owners about the management, training, and behaviour of the horses in their care. Although this questionnaire included data on horses that had not yet been trained to be ridden or had retired, this article focuses on the results of 2743 ridden horses. It reports a scale from warning signs—threatening to bite, pinning ears, tail swishing, threatening to kick or strike—to the most serious actions that include actual biting, kicking, or striking. The analysis revealed that agonistic behaviour is associated with certain management or training activities and that horses that show one form of behaviour are likely to show others in the same context. This means that some horses are particularly motivated to show these responses by certain triggers that arise in such contexts. The clusters with common characteristics were those observed in the context of: accelerating when ridden; saddling; familiar management activities; proximity to unfamiliar horses and other species. Taken together, these results highlight the prospect that the motivation to show these responses differs with context. This finding challenges the simplistic view that the problems with equine aggression and defence lie with the horses themselves rather than with historic or current management practices. Agonistic behaviours are often directed at other animals for self-defence or to increase distance from valued resources, such as food. Examples include aggression and counter-predator behaviours. Contemporary diets may boost the value of food as a resource and create unanticipated associations with the humans who deliver it. At the same time the domestic horse is asked to carry the weight of riders and perform manoeuvres that, ethologically, are out-of-context and may be associated with instances of pain, confusion, or fear. Agonistic responses can endanger personnel and conspecifics. They are traditionally grouped along with so-called vices as being undesirable and worthy of punishment; a response that can often make horses more dangerous. The current study used data from the validated online Equine Behavioural and Research Questionnaire (E-BARQ) to explore the agonistic behaviours (as reported by the owners) of 2734 horses. With a focus on ridden horses, the behaviours of interest in the current study ranged from biting and bite threats and kicking and kick threats to tail swishing as an accompaniment to signs of escalating irritation when horses are approached, prepared for ridden work, ridden, and hosed down (e.g., after work). Analysis of the responses according to the context in which they arise included a dendrographic analysis that identified five clusters of agonistic behaviours among certain groups of horses and a principal component analysis that revealed six components, strongly related to the five clusters. Taken together, these results highlight the prospect that the motivation to show these responses differs with context. The clusters with common characteristics were those observed in the context of: locomotion under saddle; saddling; reactions in a familiar environment, inter-specific threats, and intra-specific threats. These findings highlight the potential roles of fear and pain in such unwelcome responses and challenge the simplistic view that the problems lie with the nature of the horses themselves rather than historic or current management practices. Improved understanding of agonistic responses in horses will reduce the inclination of owners to label horses that show such context-specific responses as being generally aggressive. [ABSTRACT FROM AUTHOR]