This is one of the most difficult issues for all of us because of the connection between opinion and knowledge or certainty. Much less attention has been given to the question of what opinions are, and much more to how to ascend from them to knowledge.
In our own time the problem is largely neglected because of the assumption that the authority of the experimental sciences, and the standard of testing, settles the matter of what counts as real knowledge. Even though it, the modern science, has no moral content, and so is profoundly wanting from the ancient perspective or the perspective of metaphysical science.
In an ethical context opinion is very problematic because to condemn a person to death on an opinion seems wrong. If opinion implies that there are other opinions, including one where the one on trial is not found guilty or not found deserving of death.
For metaphysics the problem is very great because even the distinction between matters of moral importance, and matters that are not, is either a matter of opinion or knowledge. In our own time a large number of issues of daily life are regarded as outside the realm of ethics or morals. Whereas, in former times, the whole of life was considered an ethical question as it still is among traditional peoples and those who live under religious orders rather than liberal.
The shadows of Plato are the classical expression of the problem. We rely on the shadows, but aspire to the truth above. Aristotle, the great doxologist, puts vastly more weight on the opinions of the population, and correspondingly less on the claims of certain men to have more sound views. Especially Socrates with his wild claim that Justice is what makes men better, a general opinion, much contradicting the more widely held opinion, that Justice concerns chiefly contracts and property or giving to each what is theirs.
The issue of raising an equivocation when speaking shows a philosophic awareness of the problem that we don't know if our views are truths. One often absent in political people and the so-called boasters which Socrates discloses.
"The fundamental cause of the trouble is that in the modern world the stupid are cocksure while the intelligent are full of doubt." Russell