This question is often posed by many as a “Gotcha!” question to try to trip up Christians as they explain God. It often becomes troublesome to many Christians and almost impossible to answer at first. First, let’s see what this question’s implications are, and then we will see its presumptions.
It implies that if God cannot create this rock then He is not all-powerful; and if He can create this rock and hence cannot lift it, then He again is not all-powerful.
It lies almost wholly on the presumption that God is all-powerful, and that definition is that God can do everything and anything. That is an incorrect assessment of all-powerful.
The definition of power ranges from strength, to force, to ability. It all centers around the energy or force of something acting upon another. Obviously, God as infinite power, force, and strength to use as God. The incorrect definition then lies with equating all-powerful, to being able to do anything.
There are several places in the Bible where God is described as not able to do something because of who God is:
“So that by two unchangeable things in which it is impossible for God to lie, we who have taken refuge would have strong encouragement to take hold of the hope set before us.” – Hebrews 6:18
“Also the Glory of Israel will not lie or change His mind; for He is not a man that He should change His mind.” – 1 Samuel 15:29
“if we are faithless, he remains faithful, for he cannot disown himself.” – 2 Timothy 2:13
“The LORD is slow to anger but great in power; the LORD will not leave the guilty unpunished. His way is in the whirlwind and the storm, and clouds are the dust of his feet” – Nahum 1:3
“When tempted, no one should say, "God is tempting me." For God cannot be tempted by evil, nor does he tempt anyone” – James 1:13
So, the Bible clearly says God will not lie, will not change His mind, will not leave the guilty unpunished, and will not be tempted or tempt anyone with evil. These are so because God is just, unchanging, and of logic.
To return to all-powerful, this would simply imply having all force and strength that is possible (logical) available to that something. The suggestion that God can do absolutely anything is illogical and contradictory since that implies God can do good and evil or allow sin to be passed over without justice done, of which He cannot. God is of order and logic and cannot create something illogical such as a two-sided triangle or a married bachelor since such are illogical and lies.
Now let’s look at what the question is asking for. A rock that is also all-powerful since God is all powerful. A rock is a material object, and material objects cannot be material and be infinite in any way, that’s contradictory. We know God cannot lie and is logical, and a contradiction is illogical and a falsehood. So, the question is demolished.
A second way to approach this question is to grant that somehow God can create this illogicality for sake of argument. You can then point out that since the rock and God has infinite power, that the rock can never be more powerful than something that already has infinite power even if it also has infinite power. Thus, their outrageous ask for a rock more powerful than infinite power is ridiculously illogical and does not bring us to the conclusion that God is not all-powerful, but that the question is flawed and misunderstands the definition of “all-powerful”.