I rather don’t like the condescending attitude but will at least applaud the use of the word “skeptic” rather than “denier”; the latter being a more religious phrasing.
Disclaimer: I do think man-made climate change is happening and something very much worth addressing. The interesting part is simply what to do about it; on which people will disagree vehemently.
In my personal opinion the definite argument for any given position on climate change (the same standard would also apply for the 'sceptics'), like any other physical domain, would be a mathematical model with decent (and not retroactive) predictive accuracy. Of course the climate is an incredibly complex system, which makes creating accurate models incredibly difficult – do we even have a quantitative model for marginal changes in the mean global temperature with respect to e.g. co2 concentration in the atmosphere at the present time? I have not paid attention in several years, but when I was reading up on this several years ago the scientists had severe problems reeling in the uncertainty in said models. Something about the sun, oceans and many different kinds of fairly local feedback systems.
Anyways, you can't argue with predictive experiments!
Disclaimer: I also think man-made climate change is happening and something very much worth addressing, and I can confirm I disagree vehemently with many well intended strategies.