What did Jesus mean when He said God isn't willing for any to perish?

I am having trouble understanding the concept of God rejecting some while showing mercy to others. In Matthew 18:14, Jesus says that “God is not willing that any should perish”. Yet this seems to refute Paul's teaching in Romans 9, where Paul says God sovereignly elects some "vessels" (i.e., people) to be saved but not others. Can you help reconcile these ideas?

The solution to your dilemma is found in considering Jesus’ words in their proper context. Here’s the full passage of Jesus’ words:

Matt. 18:12 “What do you think? If any man has a hundred sheep, and one of them has gone astray, does he not leave the ninety-nine on the mountains and go and search for the one that is straying?
Matt. 18:13 “If it turns out that he finds it, truly I say to you, he rejoices over it more than over the ninety-nine which have not gone astray.
Matt. 18:14 “So it is not the will of your Father who is in heaven that one of these little ones perish.

Notice the context is 100 sheep with one gone missing. This is essentially the same parable as reported in Luke 15:

Luke 15:4 “What man among you, if he has a hundred sheep and has lost one of them, does not leave the ninety-nine in the open pasture and go after the one which is lost until he finds it?
Luke 15:5 “When he has found it, he lays it on his shoulders, rejoicing.
Luke 15:6 “And when he comes home, he calls together his friends and his neighbors, saying to them, ‘Rejoice with me, for I have found my sheep which was lost!’
Luke 15:7 “I tell you that in the same way, there will be more joy in heaven over one sinner who repents than over ninety-nine righteous persons who need no repentance.

Jesus' context is that of a sinner who repents in comparison to 99 who are righteous and need no repentance. In the symbolism of the parable, however, it’s important to note that all 100 are sheep. Jesus doesn't describe 99 sheep and one goat who then turns into a sheep. Rather, all 100 are sheep from the start, including the lost soul. Though the person is lost, nevertheless from God's point of view the person is Jesus' sheep because he is destined to believe and be saved.

That symbology is consistent with Jesus’ words in John 10:

John 10:14 “I am the good shepherd, and I know My own and My own know Me,
John 10:15 even as the Father knows Me and I know the Father; and I lay down My life for the sheep.
John 10:16 “I have other sheep, which are not of this fold; I must bring them also, and they will hear My voice; and they will become one flock with one shepherd.

John 10:25 Jesus answered them, “I told you, and you do not believe; the works that I do in My Father’s name, these testify of Me.
John 10:26 “But you do not believe because you are not of My sheep.
John 10:27 “My sheep hear My voice, and I know them, and they follow Me;
John 10:28 and I give eternal life to them, and they will never perish; and no one will snatch them out of My hand.

In the John passages, Jesus’ language makes clear that the unbelieving Pharisees were not His sheep: not now, not ever. On the other hand, Jesus says there would be unbelieving Gentiles who were His sheep (v.16), though at that moment they were not yet believing in Jesus. That detail tells us that from God's perspective a person belongs to God long before the person believes. God sovereignly appoints a person to eternal life, and in a day to come they will believe as God appointed.

So clearly, Jesus' teaching implies that some unbelievers are elected by God to believe, and therefore they are His sheep even before God calls them into faith. They are sheep in the sense that the Lord knows them and has a day of salvation appointed for them in the future. One day those lost sheep will be found by God and believe and be saved.

Therefore, in Matthew 18 Jesus is saying that the Father wishes none of His elect (i.e., His present and future sheep) to perish. This is consistent with Paul’s teaching in Romans and elsewhere, and with Peter's teaching on this topic.