Non-specificity is a key challenge in the successful development of therapeutic antibodies. The tendency for non-specific binding in antibodies is often difficult to reduce via judicious design and, instead, it is necessary to rely on comprehensive screening campaigns. A better understanding of the molecular origins that drive antibody non-specificity is therefore highly desirable in order to prevent non-specific off-target binding. Here, we perform a systematic analysis of the impact of surface patch properties on antibody non-specificity using a designer antibody library as a model system and DNA as a non-specificity ligand. Using an in solution microfluidics approach, we discover patches of surface hydrogen bonding to be causative of the observed non-specificity under physiological salt conditions and suggest them to be a vital addition to the molecular origins of non-specificity. Moreover, we find that a change in formulation conditions leads to DNA-induced antibody liquid-liquid phase separation as a manifestation of antibody non-specificity. We show that this behaviour is driven by a cooperative electrostatic network assembly mechanism enabled by mutations that yield a positively charged surface patch. Together, our study provides a first direct link between molecular binding events and macroscopic liquid-liquid phase separation. These findings highlight a delicate balance between surface interaction patches and their crucial role in conferring antibody non-specificity.