Why can we assume that the expected value of the error term is zero? Why can we assume that the expected value of the error term in a linear regression model is zero?
This is with regard to a simple linear regression.

Because you estimate a constant term $\alpha$ in simple linear regression
$$y_i=\alpha+\beta x_i+\varepsilon_i,$$
so that $E[\varepsilon_i]\neq 0$ just means $\alpha$ is replaced by $\hat{\alpha}=\alpha-E[\varepsilon_i]$. Hence, you might as well assume the error term has mean zero.
