Why did Britain promise Palestine to Arabs and Jews? (1917)

The Balfour Declaration was signed in 1917. It set out British support for the creation of a homeland for the Jewish people in Palestine. But when the Balfour Declaration was signed, the British had already promised Palestine to Arabs as an independent state and promised the French government that it would be an internationally administered zone. Even then, most of the land was still under Ottoman control. So why did Britain make these three conflicting promises? How did it try to resolve them? And how did Britain’s strategy in the Middle East help to cause a century of conflict?