Well, it's more like your body gets better at using fat, which leaves room for the smaller amount of carbs being used to keep blood sugar high. But many keto proponents argue you in fact can convert fats to glucose:

https://chrismasterjohnphd.com/2012/01/07/we-really-can-make...

I honestly don't know enough about it to know if this makes sense, but it seems like it is significantly more complicated than "lipids cannot turn into glucose."

The meta point is: yes you will feel like shit for a little bit on a diet, your body has to adjust. If you feel like shit longer term, you may have an actual issue a doctor can diagnose and treat.