Warning, more fan theories incoming:
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So apparently Andy’s dad left the family, and if you think otherwise, you’re wrong. Hmmm…
Well, the truth behind the matter, as we’ve all come to know is that Andy’s dad was excluded because it was another human character to render. But the in-universe reason is still known only to Pixar, or maybe even they never considered the fact.
I think it’s grasping at straws to say that the lack of a wedding ring and no family photos are clear indications that Andy’s dad walked out. First of all, both instances can only be observed extremely briefly in the film; Pixar clearly wasn’t intending for this to be dwelled upon… hence why the pictures of Andy are actually concept art (not to mention, it’s only Andy, not the rest of the family - I think there’s only a picture of Molly on the mantle).
Uh no. The reason there’s been all these theories over the years is because it isn’t clear.
The size of the house is then used as evidence, but is the new house really a downgrade?
Even if it is slightly smaller, there’s no way that the viewer is supposed to take away that Andy’s mom is moving the family to a smaller home due to financial incentives. To further kill that theory, Andy and Molly now have their own rooms in Toy Story 2, which says that if anything, the new house is bigger.
What’s my theory on it? Andy’s dad is dead. The family just moved on by the time of the events of Toy Story. Although seemingly happening within a few years (see Molly), it clearly wasn’t brought up because of it having no bearing of the plot. It’s been all-but-confirmed that Woody once belonged to Andy’s dad, and Andy’s mom retains Woody at the garage sale as “an old family toy.”