This question is a classic straw man that has most Christians looking like the proverbial deer in the headlights. At best, it challenges God’s omnipotence. At worst, it undermines his existence.
First, there is a problem with the premise of the question. While it is true that God can do anything that is consistent with his nature, it is absurd to suggest that he can do everything. God cannot lie (Hebrews 6:18); he cannot be tempted (James 1:13); and he cannot cease to exist (Psalm 102:25–27). It is crucial that we learn to question the question rather than assuming the question is valid.
Furthermore, just as it is impossible to make a one-sided triangle, so it is impossible to make a rock too heavy to be moved. What an all-powerful God can create he can obviously move. Put another way, God can do everything that is logically possible.
Finally, we should note that a wide variety of similar questions are raised to undermine the Christian view of God. Thus, it is crucial that we learn to question the question rather than assuming the question is valid.
For further study, see Norman L. Geisler, Baker Encyclopedia of Christian Apologetics (Grand Rapids: Baker Books, 1999), 553–554; see also 283–288. See also Hank Hanegraaff, “Indwelling of the Holy Spirit,” available at www.equip.org.
“Do not answer a fool according to his folly,
or you will be like him yourself.
Answer a fool according to his folly,
or he will be wise in his own eyes.”