In the book of Ezra chapter10 verse 6 to 17 why was Ezra fasting?

Answer 1

In this case the immediate context provides an answer. The Israelites had married 'foreign wives' (strange wives in the KJV). The reason this was a problem was that the idolatry of Israel was specifically the cause given for them going into captivity and since the foreign wives had in the past been instruments of introducing such into Israel, they were particularly keen to deal with this issue. 1Now when Ezra had prayed, and when he had confessed, weeping and casting himself down before the house of God, there assembled unto him out of Israel a very great congregation of men and women and children: for the people wept very sore. 2And Shechaniah the son of Jehiel, one of the sons of Elam, answered and said unto Ezra, We have trespassed against our God, and have taken strange wives of the people of the land: yet now there is hope in Israel concerning this thing. 3Now therefore let us make a covenant with our God to put away all the wives, and such as are born of them, according to the counsel of my lord, and of those that tremble at the commandment of our God; and let it be done according to the law. 4Arise; for this matter belongeth unto thee: we also will be with thee: be of good courage, and do it. 5Then arose Ezra, and made the chief priests, the Levites, and all Israel, to swear that they should do according to this word. And they sware. 6Then Ezra rose up from before the house of God, and went into the chamber of Johanan the son of Eliashib: and when he came thither, he did eat no bread, nor drink water: for he mourned because of the transgression of them that had been carried away.

Answer 2

Ezra was fasting as an expression of mourning and repentance for the people of Israel's intermarriage with foreign women, which was considered a violation of God's law at that time. He was seeking God's forgiveness and guidance on how to address this issue and restore the purity of the community.