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.