Opinions are value judgements, values are based on (insert jargon for shared world views here, take your pick of Ontologies, Intersections, etc.) The systemic framework used to make that judgement is innately flawed, so all opinions being based on bad axioms are probably wrong.
The good news is that the person judging the judgement is also basing their opinion on flawed or wrong axioms, so while they can say the other person is wrong they can't actually say what is right. This is an area the Pragmatist school delved pretty deep into, culminating in Hannah Arendt.
A great example of this is Mean Girls, where the Plastics base their opinions on a set of axioms:
1. Personal status is the most important good.
2. Physical attractiveness, money and celebrity are the defining traits of personal status.
3. Style shows off physical attractiveness and money together.
4. People who are not stylish have low status.
So the Plastics attack people regularly to raise their own status and lower others', because being on top is most important. The lines of attack are on style, attractiveness and celebrity (also money which ties into those) while they ignore things like intelligence, kindness and personability as not being status raising to them.