Everything is possible for Allah, provided that what we are referring to is actually a thing. Contradictions like square circles are not things. They are just words with no meaning. By making no sense, they have disqualified themselves from even being things in the first place.
In my first ever philosophy class, the professor had a question written on an ancient piece of technology called an overhead projetor. It said, Can God create a rock that He can’t lift? She then said, “Well if He can create it, then He can’t lift it and He’s not all-powerful, but if He cannot create, then is also not all-powerful. Therefore, the idea of an all-powerful god is not possible. Now take out your syllabi…”
Unfortunately, there is no such thing as a logic mal-practice lawsuit, but there should be, because the people who use this argument make a fundamental mistake, knowingly or not. Liftability is not a property of rocks. That is the error embedded in this question. Rocks can be smooth, rough, red, black, etc. Rocks can have heights, widths and weights. ‘Liftability’ is not a category you will find in any earth science book when it comes to rocks or anything else. Whether something can be lifted or not goes back to the one lifting, not the rock.
Thus, what the philosopher is essentially saying is can God make Himself not all-powerful? It would be negating the very definition of God, which violates the logical Principles of Identity and Non-Contradiction given in Chapter Three, since the very definition of God is that He is all-powerful. This is an excellent example in how the very basic rules of logic help believers untangle common traps laid in their path.
This is an excerpt from the booklet 'Aqida for Youth.