Escalation

You could not settle this conflict. The conversation about your opposing opinions ended when your colleague felt offended and withdraw. This stands now between the two of you. You consider escalating the issue to your boss. Not such a good idea ! It will only further hurt your colleague’s feelings if you call ‘big mum or dad’. It is better to speak with each other again. Agree to disagree and decide jointly who can help you how to resolve this conflict. Maybe you both want your boss to make the judgement call. Find whatever common ground, it will be an asset for your relationship !