Why did Paul assure the Corinthians they could trust the men who came to collect their offering?
Paul assured them because the men coming, likely headed by Titus, were men of integrity. They would not mishandle the collection but would get every penny to Jerusalem for the poor saints. Paul also sent brethren ahead so the Corinthians would be ready and his boasting about them would not be in vain.
Les explains that Paul was telling the Corinthians that the men coming, probably headed up by Titus, were men of integrity, so they did not have to worry about turning over their offering to them, because they would get every penny of it to Jerusalem where it was supposed to go. Paul had been boasting to the Macedonian congregations about the Corinthians' zealousness in making these collections. He sent the brethren so that his boasting of them would not be in vain and so they would be ready. This ministering was for the poor saints in Jerusalem, who had been left destitute because of their offerings into the common kiddie beginning with Acts chapter 2.
But thanks be to God, which put the same earnest care into the heart of Titus for you.
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Why does Paul mention the men coming to collect the offering in 2 Corinthians 8:16-24?
In verses 16-24 Paul speaks of the men who would come along to pick up the offerings, showing the need for integrity in handling the affairs of God.