Your friend’s argument starts from a false premise. “God is everywhere” is an incomplete statement of the truth. God is everywhere He wishes to be. Who are we to say where God wishes to be?
However, this is not the only approach you could take with this logic. I believe the Catechism defines Hell as separation from God’s love, not merely separation from God. So, it would be conceivable that even present in Hell, God could honor our wish to withhold His love from us.
Or, you could employ some deductive logic of your own.
A. God is always present in our lives.
B. We do not feel God’s presence in some times of distress (although it is present).
C. Therefore, it is not God’s presence that is lacking, but our inability to feel His presence, or our choice to ignore it.
So, since those in Hell are there by a conscious separation from God, in Hell they continue to choose to not recognize His presence and love - not that He is not present, or not loving.