In a container, you should be able to read a book by pressing X (with an Xbox controller) / square (for PS4) for the Actions menu, left stick to highlight Read and then A / X to select.
Did you try hitting the button to bring up the menu, even if it isn't listed as one of the actions? Does closing the container and opening it again help? If you take the item out of the container can you read it then?
Is there anything in particular that causes this problem, or does it happen randomly?