He said to them, “Go into all the world and preach the gospel to all creation. Whoever believes and is baptized will be saved, but whoever does not believe will be condemned. And these signs will accompany those who believe: In my name they will drive out demons; they will speak in new tongues; they will pick up snakes with their hands; and when they drink deadly poison, it will not hurt them at all; they will place their hands on sick people, and they will get well.” Mark 16:15-18
Jesus made this statement after his resurrection in Mark 16. He was driving home a point that those who follow him and do his will could not be stopped. They would be able to do some incredible things - speak in new languages, drive out demons, heal people.
But was Jesus telling people to pick up snakes and drink their poison? Why would this be necessary? The other examples in this section all have positive outcomes that glorify God. People are made well or hear the Gospel. How does handling snakes or drinking poison help anyone?
Jesus was not telling people to purposely handle snakes and drink poison but that if they did and they were doing God's will, they would not be harmed. This happened to Paul on the Island of Malta.
Paul gathered a pile of brushwood and, as he put it on the fire, a viper, driven out by the heat, fastened itself on his hand. When the islanders saw the snake hanging from his hand, they said to each other, “This man must be a murderer; for though he escaped from the sea, the goddess Justice has not allowed him to live.” But Paul shook the snake off into the fire and suffered no ill effects. The people expected him to swell up or suddenly fall dead; but after waiting a long time and seeing nothing unusual happen to him, they changed their minds and said he was a god. Acts 28:3-6
Paul used this incident to spread the Gospel and to heal many on the island.
Jesus used a similar "snake" description in Luke.
He replied, “I saw Satan fall like lightning from heaven. I have given you authority to trample on snakes and scorpions and to overcome all the power of the enemy; nothing will harm you. However, do not rejoice that the spirits submit to you, but rejoice that your names are written in heaven.” Luke 10:18-20
Is he telling his followers to find snakes and scorpions and step on them? What purpose would that serve? Jesus said - metaphorically - that his disciples have power over the things that could harm them. He said don't focus on your power over the spirits, but that you are saved.
Snake handlers focus more on the power of the snake handling than on their salvation. It's all about the show.
Mark 16, which makes the most significant statement about the snake handlers, appears in a section of Mark that many of the recently discovered archaeological manuscripts of Mark don't include. It apparently was added later (one of only a few such glitches in the Bible) and would be considered suspicious. Possibly Mark (and Peter who Mark was close to) did not write this in his original.
So snake handling has no real need to bring others to Christ. We just need to be encouraged that if anything deadly were to get in our way, that God could protect us if it were his will.