It is interesting the way the Lord distinguishes between the gentiles and the Israelites. We read a verse like this without noticing the distinction made:
Mosiah 3:9 And lo, he cometh unto his own, that salvation might come unto the children of men
The phrase “his own” used here refers to the Israelites. He speaks of them as “his” people frequently in the scriptures.
True, the gospel has gone to the gentiles. But I think that the Lord makes no mistake when he calls those of the house of Israel “his own”. When did they become his? Being an Israelite is something they are born into. Consequently they became his not here, but in the premortal life. They were close to him, they were particularly obedient to him, so much so that he came to call them “his own”, and continues to do so here. Certainly, they can cast that off here in mortality as many Israelites have done. And the gentiles can repent as Ruth, and obtain choice blessings beyond measure. They can become “his own”.
But, as Joseph Smith taught “Thus after this chosen family had rejected Christ and His proposals, the heralds of salvation said to them, “Lo we turn unto the Gentiles;” and the Gentiles received the covenant, and were grafted in from whence the chosen family were broken off: but the Gentiles have not continued in the goodness of God, but have departed from the faith that was once delivered to the Saints, and have broken the covenant in which their fathers were established (see Isaiah 24:5); and have become high-minded, and have not feared; therefore, but few of them will be gathered with the chosen family. Have not the pride, high-mindedness, and unbelief of the Gentiles, provoked the Holy One of Israel to withdraw His Holy Spirit from them, and send forth His judgments to scourge them for their wickedness? This is certainly the case.”