You've asked a great question. How could someone believe something so insane?

The answer is: the "deniers" don't exist. They're a strawman thrown up to help dismiss climate skeptics' without discussion. It's the kind of absurd mischaracterization that you'll always see when the media, as a group, want to destroy one side of an argument.

Real climate skeptics don't 'deny' climate change. They ask questions like:

• Could climate change be less severe than portrayed in media?
• To what degree is the changing climate caused by humans, and to what degree is it a continuation of natural processes?
• How much should we focus our efforts on simply reducing emissions, and how much should we focus on other strategies like mitigation, or simply growing human wealth so fewer people are vulnerable?
• Are there technologies that can reduce the impact of increased CO2, saving us from having to simply consume less?
• Are there conflicts of interest in climate change research and its relation to the media? How would we know? Who is investigating this?
• Is climate change falsifiable at all in the current morally-charged climate? Hypothetically, if climate change was not a real concern, how would we know?
• Given our goal is helping humanity at large, are there better places to spend our resources than this? Fighting malaria? 3rd-world nutrition? Education of women in rural India? Scanning for world-destroying asteroids hurtling at us?

I'm not offering answers to any of these. I'm just noting that these are really important questions to talk about. But they don't have black-and-white moralistically-charged answers, which is probably why they're mostly ignored and this whole discussion is instead reduced to a game of "hate the infidels".