Saying we won’t have a habitable planet by century's end specifically because of climate change is definitely a falsehood (except for the technical point that 100% and 0% are not real probabilities). Saying some regions won’t be habitable is correct, but it always has been even before the industrial revolution.
I certainly expect things to get worse before they get better, but “by century’s end” is too far away for even better/worse to be predictable to high certainty: there are 78 years from now to 2100, and it was only about 73 years between the president of the Royal Society, Lord Kelvin, saying “I have not the smallest molecule of faith in aerial navigation other than ballooning or of expectation of good results from any of the trials we hear of”[0] and Apollo 11 landing on the moon. What’s going to happen between now and then? A crop of GM phytoplankton with super-photosynthesis that stabilises atmospheric CO2 at 200 ppm? Von Neumann machines disassembling the moon and turning it into a ten billion O’Neill cylinders? A bioweapon that turns all humans stupid? Plain old global thermonuclear war? All of the above? No way to tell.
It's only a falsehood if you live in Scandinavia or East Asia. What about the hotter parts of South East Asia which are on the cusp of survivability as is?
How can a prediction be a lie? Worst case scenario places like India become inhabitable. India being a nuclear armed country isn't going to stay in place and die.
But it's a falsehood, and it becomes a lie when you share it, so maybe keep your delusions to yourself next time.