The largest problem, from a logical standpoint, is that
experiments are not always possible. In many cases, we are
limited to observational studies. We have to observe the
variables as they occur naturally, outside our control, and try
to find the relevant correlations.
Under the right circumstances, an observational study can provide
evidence of causality. However, it has two major drawbacks in
relation to an experiment.
First, it does not involve random assignment to experimental and
control groups. So there's a danger that any correlation we find
between two variables may be due to some third variable which is
not evenly distributed among the groups.
Second, an experiment allows us to control one variable and look
for changes in another. If we find them, there is no question
which is the cause, which the effect. This question, though,
does arise in observational studies. There is always the
possibility of confounding variables.