The Curious Incident of the Dog in the Night-time 3

It doesn't make sense for father to lie about mother leaving. I feel like this will make Christopher afraid because he tells him to tell the truth and then lies to him.  I feel like there is no reason to do this especially brcause his mother is trying to keep in contact with her son.  It also makes me feel bad for mother because she felt like she wasn't needed and thats why she left.