Thank you for the question about Codex Sinaiticus, “Why did the Codex Sinaiticus exclude the book of Hosea?”
In my reading about Codex Sinaiticus, there are large sections of the Old Testament that are missing. The New Testament and the Apocrypha has been preserved in this Codex.
If one is focusing on one particular book, the Book of Hosea, there may be historical document regarding the absence of this book. The specific reason is unknown to me.
Having said that, one can or may conjecture why the Church Fathers questioned the canonicity of Hosea. As one reads this book, Hosea is told to marry a prostitute, named Gomer. She becomes unfaithful and leaves him. God calls him to take her back as his wife. Can it be that the Church Fathers did not want the listener to think that it is acceptable with God if one is unfaithful to one’s spouse or to marry someone of immoral background? It appears that God is condoning immorality. That is not the case.
Gomer is an illustration or analogy of Israel’s faithfulness to God. God chose her to be his precious bride. The Israelites worshipped other gods, running after them while deserting God. God continues to call Israel to himself, but they are stubborn and refuse to repent of her sinful ways. Her stubbornness will lead to God’s discipline of her including exile from the Promised Land. God’s discipline doesn’t mean that he rejects Israel. It is to reform her. God’s love is unconditional despite Israel’s spiritual idolatry.
The Church Fathers may have failed to understand or to emphasis spiritual idolatry. They may have been thinking more of physical immorality. Thus to avoid the potential of believers thinking that it is acceptable by God to commit sin, they may have decided not to include or not to read Hosea. That is a conjecture on my part.
-Kingston