NO NO NO I am wrong!
You can only catch threadworms from other children, cats have roundworm, but you can catch them, apparently:
Can Roundworm spread from cats and dogs to children?
Roundworm are the most common parasite of the digestive system in cats and dogs. Roundworm can only spread to humans by ingesting roundworm eggs. This can happen when a child comes in contact with contaminated soil or sand and then transfers eggs to the mouth via contaminated fingers or by putting contaminated objects in their mouths.
Visceral larva migrans, is a disease caused by roundworm that can affect humans.
Visceral larva migrans also known as Toxocariasis is a potentially serious disease that can affect the eyes and other organs. The disease is caused by Toxocara canis (dog roundworm) which lives in the intestine of dogs and Toxcara cati (cat roundworm) which lives in the intestine of cats. Dogs have been known to be infected with Toxcara Cati after eating the feces of cats.
After the eggs are inadvertently eaten they hatch in the human intestine. The larvae from these eggs are then released into the bloodstream and find their way to all parts of the body, including the liver, lungs, heart, brain and eyes.
Most human patients are children between the ages of two and four years, who become infected after playing in sandboxes or soil contaminated by pet feces. The eggs can survive in soil for as long as seven years.
Toxocariasis can be prevented by keeping children from playing in soil contaminated by animal feces and by teaching children to wash their hands before eating. Toxocara eggs can only become infective if they have been in the environment for approximately two week, so direct contact with an infected animal generally does not result in transmission.