Why did the Big Three (Churchill, Roosevelt, and Stalin) distrust each other?

I am not sure if the relationship between Churchill, Roosevelt, and Stalin was essentially that of mistrust. After all they were collaborating and cooperating for achieving the common objective of defeating Germany led by Hitler.

Most certainly, in international politics, heads of governments of countries are not expected to absolutely open in disclosing their thinking and long terms objectives. In spite of their common interests, the different countries and their leaders do have other independent objectives, which may conflict with the common agreed objectives.

For example, while Stalin may not openly disclose his resolve to support communism, Roosevelt may not have disclosed his resolve to oppose communism.

However we can say that whatever differences existed between the three were because of the conflicting long term interest of the three countries, and the difference in their political ideologies. But such things are often known to people fairly well, and because of that some distrust to exist between people with conflicting interests and approaches is quite natural.