This is something I've come to understand better over the last year. To understand how I got there, let's first take a little side-trip.
The Nature of God
Think about who God is: the ultimate being, the creator of the universe, all powerful, all knowing, all encompassing. As humans, we cannot possibly begin to understand such a being: his motives, plans, or desires. We have only three ways to understand Him: those limited aspects revealed to use through the Holy Spirit, Scripture, and through studying His creation.
In Scripture, God reveals to us ultimate outcomes regarding our behaviors, attitudes, and loyalties. On the one hand, we can align with God and attempt to live the kind of life modeled for us through Jesus in scripture; the outcome is heaven. On the other hand, we can do whatever we want without regard for God; the outcome here is hell, even if doing whatever we want results in living as a "good" person.
But what if God's lying? God has the same moral obligation to us that we would to a small colony of ants, because we are so insignificant by comparison. In fact, it's even less than that, because without God our little "ant colony" lives would never exist in the first place. It would not be immoral for him to use us as pawns in some sort of cosmic game beyond our understanding. How are we to know that we have any hope at all beyond this life? That anything revealed in scripture will last?
Thankfully, scripture also addresses this issue, if indirectly. In scripture, God is carefully presented over and over and over as a being that keeps his promises, and deals only in truth... often even across generations and hundreds of years.
Genesis and Faith
So back to the question. Genesis is understood by a great many Christians to be God's personal account, revealed to Moses, of what He did at Creation. If God lied to Moses, it undermines everything else we understand about who He is. If God lied to Moses here, is he also lying about what happens after we die? As 1 Cor 15 says, if our hopes depend on an "if" such as this, we are to be pitied. Can we be sure any longer that there's any advantage to remaining a loyal Christian? Genesis needs to be an honest account of Creation, or everything else begins to unravel.
That should cover the actual question. Theistic Evolution creates theological problems because it can undermine the whole of everything else Christianity asks you to believe. It is possible to go through your whole life believing in Theistic Evolution and a fully allegorical account, but it forces you take a piece of scripture that is seemingly written to be literal and interpret it in an allegorical way, and this can erode Faith over time.
How do we resolve the seemingly-strong naturalistic evidence for Evolution with the seemingly literal Creation account? There are a few options.
The first is that we believe in a God who is big enough to "fake" the evolution evidence, as another kind of cosmic joke. I think most Christians believe God has that kind of power and more. However, this again falls outside of what we understand of His nature, and would undermine Faith no less than would simple Theistic Evolution. God could do this, but I don't know many who believe that is what actually happened.
The second option is that Moses lied. This is tempting, but it doesn't get us very far because most Christians also believe Scripture to be inspired. If Moses lied, and the lie was allowed to remain part of scripture, this again undermines much of the rest of what we believe.
Another possibility is that the evidence is wrong, incomplete, badly-misinterpreted, or some combination thereof. Any real scientist needs to admit to this possibility, as that is what makes science, science; there is no such thing as "settled science." Personally, I think there is some of this, but that it's not the whole story. For example, if you carefully read the Genesis account you see that order of Creation is incredibly close to the order of Evolution... but not an exact match. It would not surprise me that at some point in the future new fossil finds will require the Theory of Evolution to adjust the proposed order to match Genesis, or that such fossils may have once existed but are now lost to us forever.
A fourth possibility is that we have historically made a flawed literal reading of the Genesis creation account. I've covered this in a few other answers, but it comes down to the biblical definition of the word "day". We often take the sections that read "and evening came, and morning. The [Nth] day" and apply the modern 24-hour definition to that section. We forget that the ancient Jews had a very specific definition of day. It was the time from sunrise to sunset. Given the complete lack of a sun for the first several days of creation, it now becomes obvious that God must be delivering an allegorical account of what he did, because the "normal" (for the initial audience) literal definition of day had no meaning yet. For that matter, even the "modern" definition is not really 24 hours, but rather the time for the Earth to complete a rotation with respect to the sun, a timespan which may have been much different at first. This is a position that definitely encourages at least a limited Theistic Evolution.
Of course, this is not a completed position. There are still elements of the Creation account that cry out to be read literally. What about the 2nd half of the first week, after there was a Sun for use in marking days? The Creation of Man? Cain and Abel and other early humans? At the moment, I don't have a completed answer. What I do have is Faith.