Acts 10

The Lord said to the children of Israel -

"Surely the Lord GOD will do nothing, but he revealeth his secret unto his servants the prophets." (Old Testament | Amos 3:7)

There is no question, that because of covenants made, the Savior's mission was to the House of Israel. The Savior so declared, as the gentile woman approached Him of her daughter vexed with a devil, saying -

"...I am not sent but unto the lost sheep of the house of Israel." (New Testament | Matthew 15:24)

Even the woman at the well understood this saying -

"...How is it that thou, being a Jew, askest drink of me, which am a woman of Samaria? for the Jews have no dealings with the Samaritans." (New Testament | John 4:9)

It becomes clear that there are times and seasons in fulfilling the purposes of God. It is obvious, the the gospel was first to be taught tot he house of Israel. Gentiles were exclude - at lease for a season. Now with the change in season to take place in the preaching of the gospel to all nations, the Lord declared He would reveal His will through His prophets.

There is not question that Peter was the leader or President of the Church, or prophet. Cornelius was instructed to go to Peter and none else. To Peter it was then revealed that -

"...Of a truth I perceive that God is no respecter of persons..."
(New Testament | Acts 10:34)

"But in every nation he that feareth him, and worketh righteousness, is accepted with him.
36 The word which God sent unto the children of Israel, preaching peace by Jesus Christ: (he is Lord of all:)" (New Testament | Acts 10:35 - 36)

Understanding this event, does it not somewhat sound reasonabe that the Lord would, for His own reason purposes, withhold certain blessings for another group for a season. It was again through a prophet of God, just as Peter, the following revelation was given -

" Dear Brethren:
6 As we have witnessed the expansion of the work of the Lord over the earth, we have been grateful that people of many nations have responded to the message of the restored gospel, and have joined the Church in ever-increasing numbers. This, in turn, has inspired us with a desire to extend to every worthy member of the Church all of the privileges and blessings which the gospel affords.
7 Aware of the promises made by the prophets and presidents of the Church who have preceded us that at some time, in God's eternal plan, all of our brethren who are worthy may receive the priesthood, and witnessing the faithfulness of those from whom the priesthood has been withheld, we have pleaded long and earnestly in behalf of these, our faithful brethren, spending many hours in the Upper Room of the Temple supplicating the Lord for divine guidance.
8 He has heard our prayers, and by revelation has confirmed that the long-promised day has come when every faithful, worthy man in the Church may receive the holy priesthood, with power to exercise its divine authority, and enjoy with his loved ones every blessing that flows therefrom, including the blessings of the temple. Accordingly, all worthy male members of the Church may be ordained to the priesthood without regard for race or color. Priesthood leaders are instructed to follow the policy of carefully interviewing all candidates for ordination to either the Aaronic or the Melchizedek Priesthood to insure that they meet the established standards for worthiness.
9 We declare with soberness that the Lord has now made known his will for the blessing of all his children throughout the earth who will hearken to the voice of his authorized servants, and prepare themselves to receive every blessing of the gospel.
10 Sincerely yours,

SPENCER W. KIMBALL
N. ELDON TANNER
MARION G. ROMNEY

The First Presidency"
(Doctrine and Covenants | Official Declaration 2:5 - 10)