Why did the pilgrims depart from Plymouth, England before arriving at Cape Cod?

The Mayflower and its sister ship the Speedwell originally left the port of Southampton after a lengthy delay. However, due to the Speedwell springing a leak, the two ships were forced to dock at the Devon port of Dartmouth for much-needed repairs. The unplanned stop added a further delay to the voyage, but worse was to follow. After leaving Dartmouth, the Speedwell sprang another leak, necessitating one more impromptu stop, this time at Plymouth, also in Devon.
There is some degree of historical controversy as to whether Plymouth was the Pilgrims' last port of call before their voyage to America finally got under way. Some historians have suggested that the Mayflower and Speedwell stopped off at Newlyn in Cornwall before continuing with their journey. However, this is very much a minority opinion, and most historians accept that Plymouth was the Pilgrims' last destination in England before they eventually reached Cape Cod.
https://www.britannica.com/topic/Mayflower-ship