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All my life I have taught, and been taught the importance of sound doctrine.
For all the reasons outlined in these excellent answers, the importance is right up there.
However, Christ redeems people of every level of ability, and every level of education. In the last year it has hit me forcibly that we are not redeemed by "sound doctrine"; we are not made one whit a better Christian by because we know "sound doctrine". True, having the knowledge enables us to follow Christ more closely; yet some people seem to love God so deeply - perhaps because they have been redeemed from such a terrible state - that their lack of knowledge is not a problem.
Don't get me wrong: Sound doctrine is an important subject every Christian should seek after: But remember, we are not saved by the Word: We are saved by Jesus, by faith in Him, and only because of His grace!
I know this may seem to be a very simplistic analogy but I can't think of a better way to express what I believe about sound doctrine.
When I was born, it didn't matter if I knew the multiplication tables or the difference between a vowel & a consonant. But I can't imagine how difficult the past 60 years would have been if I had not been taught both of these "doctrines."
And in the same way, when I was first born-again, in my early walk with Christ I had little understanding of doctrine, little knowledge of the Bible truths & only faintly understood His grace. But I knew that I was living proof that it was real.
For many years I stumbled along as a peripheral Christian until, in the midst of a time of great stress, I sought comfort in His Word. It was then that I began to understand the doctrines upon which I had established my faith.
The deity of Christ, His crucifixion and resurrection, salvation by grace, one God and His gospel.
I know that knowing these basic immovable truths won't make me a better Christian, but they do help me "work out my own salvation with fear and trembling."
Not working "for" my salvation, but contributing to it by being diligent and persevering, doing all that is to be done in obedience to His will for my life.
Not knowing sound doctrine when we are first born-again is not a sin, but it sure can be a stumbling block if we continue in that ignorance.
We should all be as those in Berea of Acts 17.
Why is sound doctrine so important? Sound doctrine is so important because it will settle us (Ephesians 4:14).