Opinion formation within society follows complex dynamics. Towards its understanding, axiomatic theory can complement data analysis. To this end, we propose an axiomatic model of opinion formation that aims to capture the interaction of individual conviction with social influence in a minimalist fashion. Despite only representing that (1) agents have an initial conviction with respect to a topic and are (2) influenced by their neighbours, the model shows the emergence of opinion clusters from an initially unstructured state. Here, we show that increasing individual self-reliance makes agents more likely to align their socially influenced opinion with their inner conviction which concomitantly leads to increased polarisation. The opinion drift observed with increasing self-reliance may be a plausible analogue of polarisation trends in the real-world. Modelling the basic traits of striving for individual versus group identity, we find a trade-off between individual fulfilment and societal cohesion. This finding from fundamental assumptions can serve as a building block to explain opinion polarisation.