The problem would not be with the doctrine of Sola Scriptura itself but with how people think. Just because people may make mistakes in math does not mean that there is something wrong with mathematical principles. We could also apply your reasoning to catholic teachings. Do you believe the teachings of the catholic church are wrong because there are catholics who don’t understand them or missapply them?
Yes but in your example are you not deciding who is thinking rightly, and who is thinking wrongly ?
Cannot I, for example, decide someone else is right and you are wrong ?
Who has authority there to decide ? Who has the authority to decide who has the authority ?
With the bible alone there is no process for that except the personal view that says - I am reading it rightly and because of that I have the authority.
This is extremely arbitrary and the vast number of people who claim that authority personally disagree on many aspects of the bible.
If you take the example of maths, before we start we have to agree on the principles and rules of mathematics.
We do not get the example of half the world thinking the answer to a mathematical problem is one thing and the other half of the world thinking the answer is something else.
I don’t believe that is a good analogy simply because with the bible we have to agree on the interpretation before we can apply it’s teachings.
It is clear that unlike mathematics, there is no agreement on its interpretation.
I think also your analogy of ‘my reasoning’ towards the Catholic church is not a good one.
It is neither right nor wrong because one or more people disagree with it.
In theory, the Catholic church could provide authoratative teachings on the bible because it has a structure of who speaks for it and under what circumstances certain teachings should be adherred to and an authority that can respond ‘in real time’ to specific and changing questions. It can decide which of conflicting biblical ideas has precedence and which are appropriate to be applied to certain circumstances. There is no structure for the bible to do that - alone.
In theory Justasking4, you also could provide a similar authoratative teachings because you also have a structure (you) and a process for interpreting (your thoughts).
Your structure however is temporary on this earth (and ends with your life) and of course your authority to speak has to be accepted by others.
People will have different criteria on accepting or rejecting your claims of authority.
The problem with sola scripture is that there is no universal, unifying structure, no process (very unlike mathematics) and everyone claims that authority for themselves.
That does not make sense to me and instead of a Covenant between God and his people we get a replacement Covenant between God and me.
Because there is so much disagreement among Christians who read the same bible, it appears that this type of covenant over time is vulnerable to become more about ME and MY interpretations and less about God.
That is how it appears to me.