The referee says that I did not attempt to "reject" my model – what does this mean?
Of course, it’s hard to be any certain without intimately knowing your work and you have to judge whether the referee’s request is any reasonable, but:
This sounds like a request for Popperian falsifiability: The referee wants you to perform an experiment, analysis, or similar that – given your a priori knowledge – could reject the model.

Obviously my null hypothesis is that my model is wrong […]

I do not find this so obvious. In many cases, a model being wrong does not pose a feasible null hypothesis, because it would have to include every alternative model. There are exceptions to this such as when your claim is that some model has predictive power and you can investigate the null hypothesis that its predictions are as good as chance. But even then, your null hypothesis is something different from “my model is wrong”.

Details: the null hypothesis is that the model does not significantly explain the data.

That does not sound like a null hypothesis. First, the word significant (in the sense of statistical testing) does not make sense within the hypothesis as it is a property of the data with respect to the null hypothesis. Second, what does your null population look like? For any given model, there is an infinity of models that are an even worse description of the data. Are they present in your null population?