Logistic regression, used in binary classification, uses the logistic function as a model for the underlying probability of the outcome variable.
It has some properties useful and essential for fitting such a model. For example it is monotonically increasing, it tends to 1 as x tends to infinity, it tends to 0 as x tends to minus infinity, it is never 0 nor 1 (allowing for positive probability of either outcome regardless of input). However, there are other options for function which satisfies these properties.
So is the logistic function used simply for convenience, or are there other motivations for why logistic function is the "correct" or only suitable function to use?