The challenge sounds reasonable enough at first - after all, we simply can't conceive of anyone making such demands and being anything other than a supremely self-centred egomaniac. Surely only the worst kinds of tyrannical dictators make such demands. But here lies the first problem with the question - it assumes that God is made in the image of man. We cannot legitimately extrapolate from sinful man to the God revealed in the Bible.
For an accurate answer to the question we need to start with God himself, as revealed in the Bible. Let me use the Westminster Confession of Faith as a handy way of summarising some of the biblical teaching about God. You can read it online here where you can check out the proof texts for yourself. The first two sections of chapter 2 read thus:
I. There is but one only, living, and true God, who is infinite in being and perfection, a most pure spirit, invisible, without body, parts, or passions; immutable, immense, eternal, incomprehensible, almighty, most wise, most holy, most free, most absolute; working all things according to the counsel of His own immutable and most righteous will, for His own glory; most loving, gracious, merciful, long-suffering, abundant in goodness and truth, forgiving iniquity, transgression, and sin; the rewarder of them that diligently seek Him; and withal, most just, and terrible in His judgments, hating all sin, and who will by no means clear the guilty.
II. God has all life, glory, goodness, blessedness, in and of Himself; and is alone in and unto Himself all-sufficient, not standing in need of any creatures which He has made, nor deriving any glory from them, but only manifesting His own glory in, by, unto, and upon them. He is the alone fountain of all being, of whom, through whom, and to whom are all things; and has most sovereign dominion over them, to do by them, for them, or upon them whatsoever Himself pleases. In His sight all things are open and manifest, His knowledge is infinite, infallible, and independent upon the creature, so as nothing is to Him contingent, or uncertain. He is most holy in all His counsels, in all His works, and in all His commands. To Him is due from angels and men, and every other creature, whatsoever worship, service, or obedience He is pleased to require of them.
Now that's quite a statement! Reading right through those paragraphs of the Confession I emerge at the other end feeling quite simply overwhelmed by the sheer majesty and unparalleled brilliance of God's character. In reading statements such as, God is 'most holy, most free' etc etc, don't forget the context set by the opening lines - that God is 'infinite in being and perfection'.
All this has an undeniable 'wow' factor. But how do we experience all of this? Is it like looking at a mighty mountain range and having your breath taken away? No - God is personal, and has from all eternity expressed these characteristics within the perfectly loving community of the Trinity. Ponder long and hard on that! An eternal, perfectly loving community. Can you grasp what that must be like, to have nothing in a relationship that is not saturated with 100% love??? We, in his creation also experience so many of God's perfect, infinite characteristics.
All in all, it is undeniable that God has what it takes to be worthy of worship - a greater, more magnificent, more beautiful being is not possible. But does he mar all that by demanding that we all pay him all our attention like a spoilt child? You may have already spotted the answer. If God is the most beautiful being possible, what else could he love most of all but himself? To love anything else would make God an idolater! Here is the great failure when we imagine God to be in our image - put any human in that position and it is undeniable egotism - because no person is that wonderful. But God is just being honest - would you prefer that he lied about what he was really like?
We must also factor in the Trinity - when we see God glorifying God in Scripture, what I find so wonderful is how each person of the Godhead doesn't seem primarily concerned with themselves, but is totally taken up with the others. (What else could you expect from a perfect community of love?) We see this pattern at work in John 17:1-5 - the Son has glorified the Father, and now the Father will also glorify the Son.
One last thought on the supposed egotism of God in calling for our worship: if God is the most beautiful being that could possibly exist, where else is the greatest joy found except in delighting in God? So is it a hardship or the supreme privilege to join with God in delighting in God? Yes, it most certainly is our duty, but there are many duties that are given to us for our own good - like going to school when we were young. What greater duty could there be than this? If you arrived in adulthood and discovered that your parents knew full well it would have been by far the best thing to send you to school, but they never bothered I think you would be justified in feeling incredibly let down. They knew their actions would lead to your leading a massively disadvantaged life, but they didn't bother to do what was good for you (even though you may have complained at the time!). So for us and God - if God really is the God of the Bible wouldn't he be failing to love us as much as he claims if he didn't insist that the greatest thing we could and should do is to delight in the most beautiful thing conceivable - that which we were created to know and enjoy? So perhaps he isn't so egotistical after all.