Chewing gum for a fasting person does not break his fast. Because it does not go inside.
If it is parted, he breaks his fast. Because some of it go inside.
It is said if there is black gum it breaks the fast. Surely it is separable.
If a woman does not fast, it is not makrooh to chew gum because that it is instead of the miswak. They do not use a miswak. Because their teeth are weak. Chewing gum gives teeth a power as much as miswak.