Chewing gum everyday or chewing too much gum too often is supposed to cause temporomandibular joint disorders.
That's rare though and I used to chew gum everyday as a teenager and nothing bad happened too me from chewing the gum everyday.
However chewing gum everyday is also supposed to cause some other health issues such as weight gain, bloating, cramping, and chronic diarrhea.
That is due to the absorption of the artificial sweeteners found in the gum and especially the sugar free gum.
I wouldn't worry about it too much though as I never experienced any of those issues when I chewed gum everyday and there's no serious health issues from chewing gum everyday.