Despite the diversity of characters filling out the cast in Toy Story, Andy's dad wasn't created. It can't be especially difficult for the filmmakers to create a dad character because they've created so many others.
Why didn't Pixar create Andy's dad character in Toy Story?
According to Craig L Good, Pixar Camera Artist, human characters were too expensive to design back then. So since a dad was not necessary for the story, Andy didn't get one.
I'm often highly entertained by the deep analyses and psychological guesswork about this. The real answer is that we couldn't afford a dad. Human characters were just hideously expensive and difficult to do in those days [...]
I believe the point of a missing father figure was to highlight the importance of Woody as an authority figure in the movie. Woody's character served as a surrogate father to Andy, whether Andy realized it or not. Also, Woody was the "father" to all of the toys, providing them structure that they otherwise lacked.
I doubt it was technical limitations (designing another character), but I do suspect it was for storytelling reasons. The main focus of the story was on the toys themselves. Only a few humans (mostly Andy and Sid, and perhaps Hanna to a lesser degree) were truly crucial to the story and the rest were mostly superfluous background noise. Adding another human with no real role to play would only add to that noise and serve as distraction.
My theory is that Andy's parents were going through a divorce that's why you never see him or gets mentioned. The toys were Andy's way to deal with the divorce.
