No sane adult would think to blame their child for their divorce. Yet children aren’t adults. They have not developed the same capacity for reasoned thinking yet. Hence, it is not uncommon to find children who believe they are to blame for their parents getting divorced.
What might lead them to believe this?
A self-centered view of the world
Young children see themselves as the center of their world. People stop what they are doing to do things for them. They cry, and someone gives them food or picks them up. They drop their toy, and the nearest person is bound to stoop to pick it up for them. They don’t yet have the logic to understand that they are just a tiny cog in the world and that most things happen irrelevant of their actions.
They can also struggle to differentiate fantasy from reality. When they tell you about the conversation they had with their pet rabbit, they are not making it up in the traditional sense. As far as their minds are concerned, the conversation happened and the rabbit really can talk.
So you can get a situation where children think something they did led to you and your spouse wanting to divorce and as unrealistic as it is to an adult, they believe it is true. For instance, they recall that a week ago they wanted to wear their favorite red dress but Daddy told them no and they started crying. Then Mommy intervened and an argument ensued that ended up with Daddy shouting at Mommy and walking out of the room. Clearly (in their mind at least) if they hadn’t insisted on wearing that red dress Mommy and Daddy would not now be divorcing.
Not all children think this of course but every divorcing parent needs to tell their child that the divorce is not their fault, just in case the child somehow believes it was.