My dentist says I need an extraction of a crowned tooth, why can't this tooth have a root canal or some other way to save it.

Thank you for posting your question.  It is difficult to give you an answer with the limited information you have given.  When was the tooth crowned?  Are you experiencing pain on the tooth?  Does the tooth have enough bone support?  What does the tooth look like on the Radiograph (X-Ray)?  Is the tooth Mobile?  What is the position of the tooth relative to the rest of the teeth? Knowing this information will be helpful in giving you an answer.  Good Luck!    

Several things can make it important to extract a crowned tooth. These include root fracture, extensive root decay, or advanced periodontal disease. All these conditions will not show by just looking on the tooth. I suggest that you further discuss the issue with your dentist. Good luck

Since you did not specify why the dentist wanted to extract your tooth, I will give a few reasons why a crowned to tooth needs to be removed. If there is recurrent decay under the crown that extends to or below the bone level, restoring the tooth may be impossible without crown lengthening. Crown lengthening requires surgery that may not be practical in your case. There may be periodontal issues such as severe bone loss around the tooth or between the roots. Another reason could be that there is a fracture in the tooth. In other words, there are a lot of reasons for extracting the tooth. Don't hesitate to ask your doctor for clarification;  you deserve to know why a treatment has been recommended!