Yup. Good luck proving it.
Arguing no one can objectively prove anything is pure sophistry
And when you run into such a person, you will rightly point that out to them. On the other hand, that doesn't help you much with someone who only argues that some things cannot be objectively proven.
It's as proven as, "the sun is hot".
I suggest you even believe it yourself, and are just arguing to argue.
Or do you really expect me to believe that you, personally believe that good nutrition is no better a life choice than good nutrition?