We can note several things from the text,
1. The family knew that Lazarus would rise again, at the general resurrection. This hope didn't solve the psychological problem of evil. They were still deeply affected, saddened by their loss, and they would have liked to have Lazarus back then, not just at the general resurrection.
1a. It's safe to assume other families who lost loved ones also would have liked to have their loved ones back. They wanted this even they also knew that they would see their own loved ones again at the general resurrection.
1b. So there's a set S of people that will be raised at the general resurrection, but families who have lost loved ones are saddened by this loss and desire to see members of this set restored to them before the general resurrection.
2. Jesus tells the family that he will raise Lazarus from the dead.
2a. Jesus raises Lazarus so that God may be glorified, so the people may see the power of God, the glory of God.
2b. Jesus brings to life a member of S, someone chosen out of S, for God's purposes.
2c. Other families were just as sad as Lazarus' family, just as pious, just as faithful, just as whatever. According to human intuitions, this might appear to show partiality or favoritism. If any mere Jew had the power to raise from the dead, he would raise his own children, and the children of his neighbor too. Jesus didn't.
2d. There's several similarities with Romans 9 here. Ultimately, this "favoritism"was to glorify God, to put him on display. Jesus elects to save Lazarus. Chooses him out of the mass of people he could have raised from the dead. To others this appears unfair, unjust, partial, unloving, and self-promoting (done for God's glory, for God's purposes, to magnify God before the people).
3. Here was one reaction to that kind of Jesus, a Jesus who chooses to have mercy on some, not all (N.B. the fact of a future general resurrection did nothing to take away the sadness or dull the pain of the loss, and other families who lost their own loved ones — just as important to them as Lazarus was to his family, they didn't love their deceased less than Mary loved Lazarus):
"So from that day they plotted to take his life."
The kind of Jesus seen here is the kind to be killed. If Jesus went around healing everyone, raising everyone, and making no distinctions and divisions, he would probably not have been in danger. Or, if he at least gave everyone the choice to have their loved ones raised, their infirmities healed, and entrance into his circle granted, ready and willing to heal and save all without exception, he wouldn't have been in danger. The Jesus presented in this text is not the Jesus of Arminianism or Universalism. He's a Jesus who choses to bring certain people to life and leave others in their death. He's a Jesus who shows "favoritism." If, say, Thomas Talbott had lived back then and had the power to raise people from the dead, he'd raise everyone from the dead. If Thomas Talbott heard that Jesu raised Lazarus, and his own child had recently died, Thomas Talbott would ask Jesus to do the same for his own child. If Jesus refused, Thomas Talbott would claim that Jesus was a moral monster. Thomas Talbott would tell Jesus that his own parents would never show this kind of favoritism, and so this Jesus could not be the messiah, could not be God.