Calculators don't solve problems, they solve equations. Writing didn't kill our memories because there's still so much to remember that we almost have to write things down to be able to retain it.
If you don't do your own research and present the LLM with your solution and let it point out errors and instead just type "How do I make ____?" it's solving the entire thought process for you right there. And it may be leading you wrong.
That's my view on how it's different at least. They're not calculators or writing. They're text robots that present solutions confidently and offer to do more work immediately afterwards, usually ending a response in "Want me to write you a quick python script to handle that?"
A thought experiment, if you're someone who has used a calculator to calculate 20% tips your whole life, try to calculate one without it. Maybe you specifically don't struggle because you're good at math or have a lot of math experience elsewhere but if you have approached it the way this article is calling bad, you'd simply have no clue where to start.