What does Mark 3:10 mean?

The Bible doesn't say if Jesus touches all those He healed when the mob swarms Him (Mark 1:33–34), but in two of His first healings, Peter's mother-in-law (Mark 1:30–31) and the leper (Mark 1:41–42), He did. For many, His touch, even the touch of His robe (Mark 5:25–28; 6:56), becomes a symbol of how to receive His healing power. Later, Peter's shadow (Acts 5:15–16) and Paul's handkerchief (Acts 19:11–12) will have the same effect.

But Jesus says that faith, not the expression of faith by touching, is what makes people well. Faith heals the woman with the issue of blood, not her touch (Mark 5:34). The faith of the centurion heals his servant (Matthew 8:5–13). And the lack of faith in Nazareth prevents Him from performing "mighty works" (Matthew 13:53–58).

The word translated "diseases" is from the Greek root word mastix. Literally, it means a whip, but as a figure of speech it means any physical or personal calamity brought about by God's punishment. At this point, the Jews still believe that illness and misfortune are punishments from God either for the sin of the person or his parents (John 9:2).

God gives us the book of Job, in part, to show us this is not the case. Job was "blameless and upright" (Job 1:8) and still God allowed Satan to kill Job's children and destroy his property. Sometimes God tells us why we suffer (John 9:3), other times He doesn't. But we can be assured that God is sovereign (Job 38), and that His actions always benefit those who love Him (Romans 8:28).