Is there a genuine benefit to using ECMAscript 6 over 5 in the applications you're building? Does this benefit actually bring any real cost-benefit/time-benefit over continuing to use ECMAscript 5?
From your colleagues perspective, there needs to be a good reason to do this. If you're working in a team, its very likely not everyone is familiar with the latest version of ECMAscript. Is it really worth expecting everyone to know the new features of this version without having any real added benefit? I honestly don't think so.
My suggestion would be to give your colleague evidence that this will improve your product. These improvements needs to be significant enough that they are a real benefit and not just saving a line of code in your application.