There are differences in the order of the books in this Bible compared to the traditional book order.
The main reasons for these differences are:
1) Some things that we need to know today are more clearly spelled out in the New Testament.
See these Scriptures which support this:
for I say to you that many prophets and kings desired to see the things which you see, and did not see them; and to hear the things which you hear, and did not hear them. (Luke 10:24 UPDV)
God, having of old time spoken to the fathers in the prophets by diverse portions and in diverse manners, has at the end of these days spoken to us in [his] Son, whom he appointed heir of all things, through whom also he made the ages; (Hebrews 1:1-2 UPDV)
For the law having a shadow of the good [things] to come, not the very image of the things, can never with the same sacrifices year by year, which they offer continually, make perfect those who draw near. (Hebrews 10:1 UPDV)
If you think of this last example, of the law having a shadow of the good things to come, it seems we would want to put the actual things first and let the shadow follow behind it, just like when light shines on the front of something the shadow falls behind it.
2) When deciding to put the New Testament first, something else seemed a little out of place. It didn't matter so much when the Old Testament was 3/4 of the way through the Bible, but now that the Bible would start with the New Testament, it seems somewhat strange to start the Bible with Matthew and the genealogy. This may have had a different meaning to Jews of that time being more into genealogies; but for our society, it doesn't seem to fit that well.
If you consider making a report or presentation, you would generally want to put your best and most important material first. Take a new believer for example. Many recommend for them to read John first. In fact, there are many publications which just have the Gospel of John as a tool for evangelism. Its style and comprehensive nature seem better suited to our culture. To put this all in perspective, say for a minute you only get one page of the Bible and had to choose between these two. Would you rather have the very rich information from the first page of John, or the genealogy and historical background from Matthew? The first page of John is so rich, you can almost say that it summarizes the whole New Testament. This makes John a better and stronger way to start the Bible.
3) The start of John is very similar to the start of Genesis (In the beginning...). This makes the New and Old Testaments start in similar ways with similar concepts.
4) The ordering of the gospels was historically found quite often in the John-Matthew-Mark-Luke order. See the ISBE entry for Mark which contains in part:
The order of the Gospels in our New Testament is probably due to the early conviction that this was the order in which the Gospels were written. It was not, however, the invariable order. The question of order only arose when the roll was superseded by the codex, our present book-form. That change was going on in the 3rd century. Origen found codices with the order John-Matthew-Mark-Luke--due probably to the desire to give the apostles the leading place. That and the one common today may be considered the two main groupings--the one in the order of dignity, the other in that of time. The former is Egyptian and Latin; the latter has the authority of most Greek manuscripts, Catalogues and Fathers, and is supported by the old Syriac.
5) It doesn't seem appropriate to start with Matthew in the UPDV since it is reconstructed. See the following web site for more information on Matthew in the UPDV: