There are two main reasons why Germany should have suffered the most deaths in WWI. These have to do with its size and the fact that it was fighting a war on two fronts.
One thing that determines how many people are going to die in a war is how many people there are to fight the war in the first place. Germany was the biggest country to be fully involved in the whole war. (Russia and the US were bigger, but Russia left the war early and the US joined it very late). Germany had about 65 million people while the UK had about 45 million and France had about 40 million. This would suggest that Germany would have more soldiers in the field, which would mean that more Germans could be killed.
A second thing that is important is the fact that Germany was fighting on two fronts. For much of the war, Germany was fighting against the British and French in the west and against Russia in the east. No member of the Allies had to face a two-front war on the scale that Germany did. Because Germany was fighting on two fronts, you would expect more Germans to be killed than, for example, French since France was fighting on one front.
These are the two main reasons why Germany sustained the most deaths in WWI.