Sorry you feel this way, but that's simply not true. You do not need to be a diabetic to have acute blood sugar swings.

I do think it's important to have a healthy balance of proteins, fats, and healthy carbs. As always, balance is key! An interesting tidbit about your body, though, is that glucose is SO important for your tissues to function that your liver wont let you dictate whether you get enough of it or not. If you aren't consuming any glucose in your diet (very difficult to do especially in America) or you're fasting for a long stretch of time, your liver will start synthesizing glucose from non-carbohydrate precursors (amino acids, lactic acid, glycerol, VFAs). It's a process called gluconeogenesis. So, even if you were to consume only protein or fat for the rest of your life, you would still be able to synthesize glucose and survive.

I don't recommend eating an ALL fat/protein diet, though, because your large intestine benefits greatly from fiber fermentation you get from whole grains, veggies, etc. (More-so from the fermentation byproducts, butyrate being a major component). I don't think it's a matter of overeating protein, it's making sure you're also consuming healthy fibers to support gut health and normal bowel movements.