You are a...
When things gets shaky, you can use me to keep it together,
Metal nails (fasteners) are inserted into objects (usually wooden) to maintain a stable structure.
but that might also get you one step closer to your demise.
The phrase "another nail in the coffin" means an event that continues a downward spiral to a bad outcome, such as toward death. (credit to Peter Taylor)
When I get close to 10 inches long, I make nice music,
Refers to the band Nine Inch Nails.
but using me on a board is far from melodic.
The sound of hammering a nail is considered loud and unpleasant. The sound of fingernails scraping a chalkboard is also horrible (credit to Peter Taylor).
Carpenters enjoy my company, but one of them might disagree.
Carpenters use nails to build objects out of wood. The "one" who disagrees refers to Jesus Christ, who was a carpenter, and eventually nailed to a wooden cross.
It is bad manners and a bad idea to bite, some one who is as hard as me
Biting one's fingernails is considered a rude and bad habit. This is also the meaning of the title. The phrase "hard as me" refers to the idiom "hard/tough as nails", which describes a strict and tough person. (credit to Peter Taylor)
You might loose some teeth, which will add to my arsenal to fight you.
Refers to the idiom "fighting tooth and nail", which means competing or fighting relentlessly without holding back. (credit to Peter Taylor)