Why do we say errors cannot be normally distributed in logistic regression

In logistic regression analysis, we mentioned that
Errors can’t be normally distributed. With proper analysis (or sound arguments) show why this is the case?
logit(P(Y=1|X))=xβ
Where P(Y=1|X)=f(x;β)=exβ1+exβ=11+e−xβ
So the loss function looks like:

∑i(yi−f(xi;β))2=∑i(yi−11+e−xβ)2
where yi’s take values 0/1.

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