1. The Doctrine of Sola Scriptura is not taught anywhere in the Bible.
Protestants often point to 2Tm 3:16 which reads, "All scripture is inspired by God and is useful for teaching, for refutation, for correction, and for training in righteousness, so that one who belongs to God may be competent, equipped for every good work." What Scripture is Timothy referring to? Obviously the Old Testament because the New Testament did not exist at this time. Further it does not say that by scripture alone man is made perfect. Timothy was a companion of St. Paul in spreading the faith. In 64 AD, St. Paul left Timothy at Ephesus to govern the Church there.
It is true that Scripture is inspired by God but only the original was which we no longer have. What we have now are countless translations and transliterations of the original with many nuances of meaning. Timothy also points out that scripture is useful to the one who teaches the faith "one who belongs to God" so that he may become competent.
On the opposite side, St. Paul urges Christians to keep the traditions as we read, "Therefore, brothers, stand firm and hold fast to the traditions that you were taught, either by an oral statement or by a letter of ours." (2Thes. 2:15)
2. Scripture interpreted apart from tradition can lead to error.
An example of this is Arius (250-336 AD), a priest of of Alexandria who began to teach as follows:
"If the Father begot the Son, he that was begotten had a beginning of existence. From this it is evident that there was a time when the Son was not. It therefore necessarily follows that he had his substance from nothing." http://orthodoxwiki.org/Arius) Therefore, Christ was not divine and equal to the Father. As you can see he used Scripture as the basis of his teaching which was contrary to the traditional teaching of the Church. The Council of Nicea condemned this as heresy or untrue.
The fact that there are many Protestant Church today, with differing beliefs is due precisely to the belief that anyone can interpret Scripture. Most Protestants believe that Christ is present only symbolically in the Eucharist. Some denominations teach that once you are "saved" you can never loose salvation. Most Protestant churches lack apostolic succession and have moved even further from tradition by ordaining women as priests and blessing same sex marriage. "How, than, can the thousands of Protestant denominations and sect all claim to be the "true Church" when their very existence refutes this claim?" (www.catholicapologetics.info/Twenty One Reasons to Reject Sola Scriptura)
3. The Bible was not available to most believers until the 15th Century.
"Essential to the doctrine of Sola Scriptura is the idea that the Holy Spirit will enlighten each believer as to the correct interpretation for a given Bible passage." (www.catholicapologetics.info/Twenty One Reasons to Reject Sola Scriptura) The presumption here is that each believer would have a Bible or at least one was available. This did not happen until the 15th Century with the invention of the printing press. This means that most Christians living the previous centuries were without final authority as to what they were to believe. This is not true, Christ gave his Church the final authority as to what was to be believed.
Christ gave this authority to Peter and his descendants when he said,
so I say to you, you are Peter,
and upon this rock I will build my church,
and the gates of the netherworld
shall not prevail against it.
will give you the keys to the kingdom of heaven.
Whatever you bind on earth shall be bound in heaven;
and whatever you loose on earth
shall be loosed in heaven. (Mt. 2:16-20)
The true church most be based on tradition unbroken since apostolic times. This same Church has expressed the tradition in scriptural form and it alone must have a visible head which can interpret scripture infallibly.