Climate change is real because the climate changes all the time just as the weather does at least as far as empirical observation goes.
It wasn't that long ago we had an ice age in terms of the history of the planet we inhabit when C02 was much more prevalent in the atmosphere than it is now.
The issue is how do we respond to climate change as the planet has warmed around 1.1 C in the past 150 years at least according to some institutions that are paid big money to as best measure these things ( often disputed by other institutions mind you ) which is nothing compared to variations in temperature over shorter periods of time even in both human and pre human history.
Warmer weather is beneficial to better food production and less deaths on average than colder weather.
Looking at these points in reverse order. Warmer weather in some places is better for food production. If you’re growing grain in Quebec, it probably makes for a more reliable harvest. If you’re trying to grow sorghum or anything else in, say Chad or Mauritania, you’re fucked because what was once fertile land is now desert. As far as health is concerned, I’d be very interested in seeing the data behind that, if you mean hypothermia kills more people than heat illnesses, I’ll take your word for it, but then throw in Malaria, yellow fever, bilhazia, trypanosomiasis all of which are tropical diseases reliant on high temps to sustain vectors, and I seriously doubt it.
In the case of climate change, you make the entirely reasonable point that climate fluctuates and has fluctuated naturally throughout the history of the planet. It has, and the planet has coped just fine - if it can survive an asteroid strike, a 2 degree rise in global temperature isn’t going to send it careening into the sun. It’s a problem with how the issue is framed that you highlight neatly. You mention the recency of the last Ice age - which ended about 12,000 years ago - the blink of an eye in historic terms. If you go back 25,000 the last global ice advance was at its most southerly extent. the largest estimate of the human population for that period that I’ve seen in a peer-reviewed scientific paper for the whole of Europe, Africa and Asia is 8 million people. The current population of the three continents is 6 billion. 25,000 years ago, the Old World population was 0.013% of what it is today. Go back to 125,000 years ago, to the ipswichian interglacial, things were a lot warmer than they are today, and we know this because we found remains of monkeys, jungle cats, and tropical elephants in ipswichian gravel deposits in the middle of London. What we don’t have is any evidence of human occupation in Britain because, it is thought, sea levels rose so fast that human beings, having retreated south during the previous ice advance didn’t migrate north quickly enough to recolonise the UK before the channel and the North Sea cut it off again. All this in a world without New York, Dhaka, Hong Kong, Lisbon, London, Singapore or Tokyo.
Climate change won’t destroy the planet - history shows us that, but what history doesn’t tell us is what happens when climate change impacts a world with billions and billions of people on it and a complex, inter-connected global economy. We need to stop with the ‘we’re killing the planet’ shit and rephrase as ‘we’re probably going to kill a lot of ourselves and make a lot more destitute, homeless and sick’ instead. I remember seeing in the Reform UK manifesto before the last election a section on climate change which was so dumb it was almost satirical but my favourite bit was the inference that everything would be fine because during Roman times it was warm enough to grow grapes in Yorkshire. Of course it conveniently left out the fact that life expectancy in Roman Britain was around 35 and one of the contributors to that was fucking malaria!