Imagine that you have the opportunity to pet a cat. In this hypothetical world cats, in general, might carry toxoplasmosis, which causes you to be more likely to pet cats, as well as having many other negative effects you disvalue greatly. The cat you may pet has been tested for toxoplasmosis, and you are very confident it is not infected and could not infect you. However, people with toxoplasmosis are twice as likely to pet a cat given the opportunity than people without it.
An EDT agent reasons that petting the cat would be reasonably strong evidence that they have toxoplasmosis, which is undesirable, so they would not pet the cat. However, a CDT agent reasons that at the time of their decision their infection status is fixed, so counterfactually deciding to pet it or not pet it cannot affect whether they have toxoplasmosis. The latter is, in this instance, more intuitively satisfying.