REASON 1 for a child's rigid thinking and behavior.
Our world operates with social conventions. The world is made up of people who interact in similar ways. Many of the children that do not naturally know how the world works socially deal with rigid behavior. This child "digs his heals in" when he doesn't understand the why's of interaction. If he doesn't know why people act as they do, he certainly doesn't know how to respond appropriately. This causes him to refuse to try, resist change or insist in something being done in a certain way.
An example of this is a child may only want to go to McDonalds and Pizza Hut when the family goes out to eat. Why? He knows what to order that he likes. There just aren't that many choices. The menu will probably be the same for the next 10 years. He knows how to order at these restaurants. He knows the questions he might be asked by the workers. It is predictable. Social situations that change are not predictable for these children.
So what is a parent suppose to do? This child needs to have new experiences but avoids them at all costs! A parent can prepare a child for any situations that are new and different. The more difficult the situation, the more preparation. Sometimes an hour before and sometimes it's six months. If the child responds to something with strong refusal, the more time is needed in the preparation phase.
The child needs to know the schedule(when), the how (a plan of how to react, interact and what to do) where (location), who(any people he needs to interact with). He may or may not need the why. He may not be able to admit or agree to the why for a long time.
A child needs exposure but he also needs instruction to maneuver through each real world situation. He has to be taught one situation at a time while helping him be successful in the social world.