At first blush many of what's known as the "I AM" statements in scripture do seem to be breathtakingly self centered or even downright ego-maniacal: "I am the way, the truth, and the life...", "Besides me there is no God...", "There is none like me...", or even, "Worship the Lord your God and serve him only."
We read these and can be brought up short by them so to speak. Who dares to speak in this way? Surely such a person would be the height of arrogance if we, as part of our ordinary everyday experience, ran into anyone in the street with such a perception of themselves. Let's step back for a moment and look at what we mean when we say "arrogant" or "boastful" though. God is not encompassed by our ordinary everyday experience after all and a little bit of humility on our part at the outset is healthy in approaching anything to do with conceptions of the Almighty.
The first definition under 'arrogance' according to Merriam-Webster is: Exaggerating or disposed to exaggerate one's own worth or importance often by an overbearing manner.
Similarly 'boastful' is defined as: "To praise oneself extravagantly in speech - speak of oneself with excessive pride boasting about her accomplishments."
So that's does it then, right? God is clearly arrogant and boastful, isn't he? Again, this is where a little humility on our part is incredibly helpful. God, if He is really God and has done what He claims, isn't saying anything but the truth in these examples. Within the Christian worldview, He IS the only Self-Existent thing; to the point that even the universe itself would cease to exist if He didn't continue to uphold it. This is precisely what C.S. Lewis had in mind with his famous "Lord/Lier/Lunatic" phrase: if what Christ said was NOT true then he is either insane or an incredibly dangerous ego-maniac on a scale that is rare throughout human history. If on the other hand, He was not either of those things, then He must have been the Lord Himself: the central and unique figure by and for whom all of reality exists. In which case, to claim anything else would be not humility but dishonesty. If knowing God and being in a relationship with Him really is the purpose for our very existence and our sole possible source of ultimate and abiding joy then for Him to tell us otherwise would be worse that dishonesty, it would be downright cruelty.
Which choice will you make? These really are the only three options, Jesus's statements don't leave open the possibility that He was simply a good example or wise moral teacher. Was he a Lunatic, a Liar, or the Lord Himself?