There are a variety of problems with theistic evolution. For example, there are exegetical problems with it, in that you’re simply not going to get theistic evolution in any fair way from the text of Scripture.
The exegetical problems are huge. The plain meaning of the text of Genesis 1 tells a story of creation within one week. Later, in Exodus, this one week creation account serves as the explanation for the weekly sabbath. Moreover, as if anticipating a possible misunderstanding about the meaning of the word “day,” Genesis 1 even provides a definition for us (evening and morning).
Yet some will still try to argue that the series of days can somehow be matched up with a big-bang cosmology and a theistic or deistic version of Darwinian evolution. It can be tough to persuade folks who have bought into that line of reasoning that they are not properly interpreting Genesis 1.
From my own perspective, the biggest problem for theistic evolution is the special creation of man. The Bible tells us:
Genesis 2:7 And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.
This special creation of man denies common descent. It affirms that man was created from the dust and then ensouled: life breathed into him by God. And yet this is only half of the problem. The other half is the creation of Eve:
And Adam gave names to all cattle, and to the fowl of the air, and to every beast of the field; but for Adam there was not found an help meet for him. And the LORD God caused a deep sleep to fall upon Adam, and he slept: and he took one of his ribs, and closed up the flesh instead thereof; and the rib, which the LORD God had taken from man, made he a woman, and brought her unto the man. And Adam said, “This is now bone of my bones, and flesh of my flesh: she shall be called Woman, because she was taken out of Man.” Therefore shall a man leave his father and his mother, and shall cleave unto his wife: and they shall be one flesh.
Like Adam, Eve was not descended from pre-human ancestors — not born to non-human parents. Instead, like Adam, Eve was specially created. That’s what the Bible says, and that’s what we ought to believe.
In my discussions with people, it seems easier to help them see that the special creation of man is inconsistent with theistic evolution, than it is to help them see that Genesis 1 is inconsistent with theistic evolution. Perhaps as you discuss this fundamental of the faith with people, you may be able to help them see that theistic evolution is wrong from Genesis 2, even if they have a firmly established misunderstanding of Genesis 1.
Perhaps you can help them to see that the theory of evolution is not based on the revelation of God, but on the foolishness of men who have turned from the Creator to the creation — with theistic evolution simply being an attempt to provide a synthesis of that worldly thought and the truth.