From The history learning site:

The Cabinet was in agreement over a withdrawal from the Dardanelle's – all except Kitchener. He considered withdrawals to be a sign of weakness that would encourage the enemy. It was the same approach that had led to a breakdown in his relationship with Sir John French at the start of World War One. Many in the Cabinet felt that Kitchener had served his purpose but now had to move on. They pressed Asquith to either sack him or push him into resigning from the Cabinet. Asquith was in a difficult position because Kitchener was still something of a talisman to the public and a sacking would not be greeted well. Kitchener spared Asquith this problem when he offered to resign in November 1915. Asquith refused to accept it believing that his public aura, regardless of Northcliffe's campaign, far outweighed the thoughts expressed by his Cabinet. However, Asquith did remove from Kitchener more of his responsibilities so that by the end of 1915, he was only in charge of administering the War Office. He finally resigned from the Cabinet when senior army commanders were given free access to the Cabinet – previously they had to go through Kitchener, which to some extent gave him control over who in the army met with the Cabinet and who did not.

It is actually quite simple. The cabinet wanted him to go. Asquith didn't but he did remove some of his responsibilities.