Why do children get diarrhea during teething?

Teething does not directly cause diarrhea. There are even other reasons. Teething usually starts around 4-6 months, exactly when you start introducing solid foods to your baby. As it takes time for his digestive system to get used to new foods, which may cause a change in the color and texture of his stool, and lead to diarrhea.
Also, around the same time, babies begin to lose their immunity, which they got from their mothers at the time of pregnancy and birth. Immunodeficiency makes them more susceptible to infection, which leads to diarrhoea.
To soothe their gums, babies start putting anything and everything in their mouths, which increases their chances of infection.