General question about Residual Variance in Linear Regression Model

Why is the residual variance the same for all values of the independent variable but the variance of the predicted y value, y hat, is not? According to my Probability and Statistics book (by Devore), the variance of y hat is "smallest when x* [the particular value of the independent variable] = x bar [the mean value of the independent variable] and increases as x* moves away from x bar in either direction".

The quote make sense. What doesn't make sense to me is that the residual variance is the same for all x* given that the residual is calculated from y hat (y hat - y sub i). What am I missing?

Thanks!