The second reason though is quite the opposite: the centurion feels he is so much less important than the one he is asking a favor of that he sends important Jewish leaders as his messengers, asking and expecting Jesus to respond without putting Himself out by coming to the house. It's much more like the president recognizing the greater importance of the citizen and realizing that individual might reasonably not consider the president important enough to see. Rather than put the important individual out, the president might send his most important representatives to request the favor. This seems an impossibly unlikely example, yet the Roman centurion's authority was such that it was impossibly unlikely in his case also.
I've always seen the centurion's faith, praised by Jesus, as being in Jesus' power to heal the servant without seeing him in person. Yet there is another level: the centurion is honoring Jesus by expressing faith in His authority and importance as being so far greater than the centurion's own (which was considerable) that he sent the most important people he knew as messengers to an even more important Person to ask his favor on the centurion's behalf. The only reason such an important figure would communicate that Jesus was too important for him to meet in person was a recognition of Jesus' authority as the Son of Man. The centurion would never have done such a thing toward an ordinary Joe. But what is his importance compared to the King of the Universe? Anyone on earth who recognized Jesus as God Himself would realize that there is no individual more important than Him. The president of the most important nation in history would not be worthy of summoning the Creator to his doorstep. The centurion recognized this in Jesus like no one else. He was requesting a favor of Him, but requesting it as one inferior, not as an equal or a superior. No matter how important or insignificant you think you are, it would be worthwhile remembering your true position before the Lord of lords and King of kings.