Hi Jess,
Like fish, axolotls have a slime coat over their skin that serves as a shield against their environment. Touching them (fish or axolotls) can damage this coat, making them vulnerable to various infections. I also find that their skin is very delicate and easily damaged.
If you need to touch your axolotl (e.g., to move it into a container), do so as quickly, gently, and briefly as possible. They aren't really pets in the sense that you can pet them.
At the risk of being pedantic, I will also note you should always wash your hands and forearms very well (and rinse off the soap very well) before putting your hands in the water, much less touching the axolotls.
-Eva