General Ritchie was concerned about the losses they would take if he ordered the Tobruk garrison to fight its way out to the east. He thought that the prospects were better to simply withdraw more forces into the Tobruk fortress and hold it under siege. The problem was that General Auchinleck was opposed to that course of action, although that was what Churchill expected them to do.
Churchill opposed abandoning Tobruk, as Auchinleck was prepared to do. He had seen the ability of troops in the fortress to resist assault and thought that they could do the same thing again. Auchinleck still wanted to hold a line west of Tobruk and fight there, outside of Tobruk. Auchinleck, in the face of questions from the Prime Minister accepted that Tobruk might be surrounded, if only temporarily. This is based on the account in Vol.III of the Official History.