Newsflash! We're in an ice age right now. Your theory is baseless. The Quaternary glaciation is the current ice age. It began 2.58 million years ago to the present.

The often repeated, half-baked argument for “current climate change is natural” is the theory that needs a realistic explanation, not the other way around. If it is "natural," then how can you explain such high CO2 levels produced by humans having no impact whatsoever?

Yes, there's a cycle. However, going back several hundreds of thousands of years, temperature swings of the glacial/interglacial cycles were a shockingly SLOWER order of magnitude than the warming rate we're currently experiencing. https://en.wikipedia.org/wiki/File:2000_Year_Temperature_Comparison.png

Outside of catastrophic geological events like the Paleocene Eocene Thermal Maximum (period of massive carbon injection into the atmosphere when earth was ice-free) there are no known precedents - natural or otherwise! - for warming this fast globally.