A part of the Bible's ingenuity is that a child can paddle in it and not drown, yet a philosopher can scuba dive in it and never fully map out its depths. It is a fantastically well-designed book that is designed to be easy to study, but also, diligence in that study is essential (2 Timothy 2:15).
Those who do not study will inevitably stumble over even the simplest of verses. This often happens because rather than studying, they focus entirely on one or two verses. One such example is the infamous self-mutilation verse: "“You have heard that it was said to those of old, ‘You shall not commit adultery.’ But I say to you that whoever looks at a woman to lust for her has already committed adultery with her in his heart. If your right eye causes you to sin, pluck it out and cast it from you; for it is more profitable for you that one of your members perish, than for your whole body to be cast into hell. And if your right hand causes you to sin, cut it off and cast it from you; for it is more profitable for you that one of your members perish, than for your whole body to be cast into hell." (Matthew 5:27-30).
Here, Jesus seems to suggest self mutilation in order to avoid temptation. Yet, typically, Christians almost never seem to interpret it this way. It is said that Origen Adamantius may be an exception, having allegedly castrated himself to curtail his sexual lusts, but there is a noticeable absence of blind, limbless Christians from the dawn of the Church to this very day.
This prompts atheists to ask why? If Jesus says we should cut off our hands to get into Heaven, why are Christians not cutting off our hands to get to Heaven? The simplest answer is it is for the same reason we don't sit at home waiting for Jesus to knock on our door (Revelation 3:20), hunt Him down to eat His flesh and drink His blood (John 6:53), or look for a narrow path ending in a narrow gate in order to get to Heaven (Matthew 7:13-14). Jesus' teachings are littered with some very obvious metaphors, which simply cannot be literal. Jesus called Himself the bread of life (John 6:35), the true vine (John 15:1), the door of the sheep (John 10:7). He called us sheep, and Himself the good shepherd (John 10:11-18). We don't need anyone to tell us "hey, He was speaking figuratively here", it's obvious (unless you're a Catholic, at which point the bread of life thing is taken weirdly literally).
But although it's quite obvious that all of this stuff is figurative, some people need us to explain that to them. Thankfully, in John 16, the Bible does that for us. "“These things I have spoken to you in figurative language; but the time is coming when I will no longer speak to you in figurative language, but I will tell you plainly about the Father. In that day you will ask in My name, and I do not say to you that I shall pray the Father for you; for the Father Himself loves you, because you have loved Me, and have believed that I came forth from God. I came forth from the Father and have come into the world. Again, I leave the world and go to the Father.” His disciples said to Him, “See, now You are speaking plainly, and using no figure of speech! Now we are sure that You know all things, and have no need that anyone should question You. By this we believe that You came forth from God.”" (John 16:25-30).
Note the surprise of the disciples as Jesus speaks to them plainly. "Ah, now you speak plainly, so now we are sure that you know all things." As if up to this point, there were some doubts, and Jesus wasn't entirely straight with them. With the hindsight we have, we see what the original audience did not. Thus, ironically, we understand Jesus better in the 21st century than His immediate followers did before He was crucified. Even more ironically, He would occasionally say things like "...Tell the vision to no one until the Son of Man is risen from the dead" (Matthew 17:9), and they would ask what it meant that He would rise from the dead (Mark 9:10). Thus, He would speak in such shrouded language that it was almost reasonable for them to assume He was speaking figuratively here, too.
Throughout Scripture, we see that this had a purpose. He wasn't speaking figuratively because He just happened to like poetry. Rather, this particular portion of His ministry required it. Paul, for example, tells us "But we speak the wisdom of God in a mystery, the hidden wisdom which God ordained before the ages for our glory, which none of the rulers of this age knew; for had they known, they would not have crucified the Lord of glory." (1 Corinthians 2:7-8). In other words, while Jesus had to lay a foundation for what was to come, revealing too much to the wrong people would have actually prevented it from ever happening. Our very salvation depended on Jesus being cryptic.
But as cryptic as He often was, Jesus was never so difficult to understand that we cannot be reasonably expected to understand the self-mutilation passage. This is the entire reason atheists are the only ones who so frequently make this mistake. Christians have never run around mutilating ourselves because we understand that Jesus is actually explaining the severity of sin to us. This statement, and others like it, are not telling us to literally cut ourselves up, but to be on guard against sin.
Another of Jesus' parables may actually be useful to us here. Found in Matthew 13:3-9, Jesus tells a story about a sower who scatters seeds. Some of it falls by the wayside and gets eaten by birds, some of it lands in shallow soil and gets burned by the sun because its roots don't go deep enough, some of it falls among thorns and gets choked out, and the rest lands in fertile ground and produces fruit.
In verses 18-23, Jesus explains the meaning of this parable. In particular, verse 22 says "Now he who received seed among the thorns is he who hears the word, and the cares of this world and the deceitfulness of riches choke the word, and he becomes unfruitful." The cares of this world, and the deceitfulness of riches, are things we can do without. It doesn't matter if we're rich in this life if we just end up going to Hell anyway. It's the same principle.
Now, the consistent message of Scripture, from Genesis to Revelation, is that salvation is by grace alone, through faith alone. If your eyes, your arms, or your legs could cause you to sin, you would still be saved if you confess Jesus as Lord and believe in your heart God raised Him from the dead. And of course, ultimately, since it isn't these things that cause you to sin, but your own heart (James 1:12-15), it wouldn't even be practical. We could cut off every non-essential body part we have, yet still sin. But if salvation is by faith, then our cutting attention should be towards that which threatens our faith. The lies of the evil one. The desire to avoid tribulation. The cares of the world and deceitfulness of riches.
So, what if I am given to alcohol, yet my faith tells me not to be drunk with wine? The conflict may cause me to leave the faith. So, what do I do here? Ditch the drink. It's difficult to do, but worth doing, because it is better to enter life "maimed" than to go down to Hell "whole". What if I become besotted with a woman, and she likes me too, but she asks me to choose between her and my faith? I can live without her on this Earth a lot more than I can live without Christ. What if, when I became a Christian, I was gay, but later discovered God is opposed to this? I can drop the faith and follow my pleasures, but it is far better to make the deep, personal sacrifice and choose Christ instead.
Thus, cutting off the right arm doesn't mean literally, any more than the Proclaimers would literally walk 500 miles and walk 500 more just to be the man who walked a thousand miles to fall down at their lover's door. I would do anything for love, but I won't do that... Cheesy song references out of the way, it's an obvious metaphor with an obvious meaning. It means that if anything could pull you away from Christ, get rid of it before it does. You can suffer these losses. You can get rid of material possessions, you can get rid of people, you can even, if it comes down to it, lose life or limb. And many Christians, sadly, did. They never cut off their own body parts, but the unbelievers were all too happy to do it for them. Nevertheless, they chose Jesus, because as the saying goes, "you can take my head, for I have a God who can give me a new one."
Thus we see that the all too common atheist interpretation of this verse is so common among them, but not among us, because ours just makes more sense. But ultimately, atheists tend to know this, because their eyes are, indeed, causing them to sin. Deceived by the devil, fearing tribulations, following riches and other worldly things, atheists do not take as much pleasure in the Gospel as they should. Thus, they will resort to twisting the very word of God in order to avoid following it. But while there is still breath in their lungs, even these may be forgiven. It takes but one successful seed. It is my hope and prayer, and my advice to atheists, that each of them will take the seeds sown by Christ, and grow into fruitful grounds.