A dog’s aggressive behavior is influenced by external and internal factors, including its psychological profile. In this study, dogs’ and owners’ personalities and the owners’ attachment style to their dogs were identified and associated with owner-reported dog aggression towards humans and animals. Forty Slovenian owners participated with their dogs, of different breeds and aggression history, sorted into three groups (non-aggressive dogs, dogs aggressive towards humans, and dogs aggressive towards animals). The owners filled out three separate questionnaires that assessed dog aggression history towards different targets, owner’s personality and degree of insecure attachment styles to dogs; namely anxious and avoidant attachment. Dog personality was characterized using a standardized dog mentality assessment test, during which the dog was exposed to nine tasks, performed outside, and dogs were scored based on behaviors they exhibited. The results indicated that dogs which were aggressive towards humans were less sociable than non-aggressive dogs and this was associated with the higher neuroticism scores of their owners. We also found that dogs which were aggressive towards strangers had owners with lower scores for anxious attachment and that dogs which were aggressive towards owners had owners with higher scores for avoidant attachment. These results imply that the psychological profiles of both a dog and its owner influence dog aggression towards humans.