Most dental insurance covers the cost of a tooth extraction or at least part of the cost of a tooth extraction.
If your tooth extraction is needed because it's urgent and becomes a health issue then the dental insurance or even other health insurance coverage should pay for the cost of the tooth extraction.
Dental insurance also usually covers the cost of preventative dental care and things such as fillings, crowns, root canals, and oral surgery.
If you just go in for a teeth cleaning or other non medical dental need then the dental insurance will usually not cover the cost of the dental visit.
But for a tooth extraction that's deemed necessary the dental insurance should cover the cost of it or at least cover part of the cost of the tooth extraction.