Why do doctors use a new thread for each stitch?
Using a single thread for a suture also known as continuous stitching has a major con that it has higher risk of failing if the suture is cut in just one place. So it is generally avoided eventhough it is very easy to do. 

On the other hand interrupted stitching ( one thread for each stitch) is favoured because of lesser risk of failing, eventhough it is time consuming than continuous stitch.

Source:https://en.m.wikipedia.org/wiki/Surgical_suture