There is a series of connections that bring about the thought that we (humans) could not have evolved.
From Paul's letter to the Romans (chapter 5)where he describes the way to Salvation:
9 Since we have now been justified by his blood, how much more shall we be saved from God's wrath through him!
10 For if, when we were God's enemies, we were reconciled to him through the death of his Son, how much more, having been reconciled, shall we be saved through his life!
11 Not only is this so, but we also rejoice in God through our Lord Jesus Christ, through whom we have now received reconciliation.
12 Therefore, just as sin entered the world through one man, and death through sin, and in this way death came to all men, because all sinned—
13 for before the law was given, sin was in the world. But sin is not taken into account when there is no law.
14 Nevertheless, death reigned from the time of Adam to the time of Moses, even over those who did not sin by breaking a command, as did Adam, who was a pattern of the one to come.
Then add John 3:16 --- "For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life."
The idea of sin being the cause of all death (God's curse on the earth) throws out evolution because death is required for "desirable" traits to become dominant in the animal populations.
Therefore, if you don't believe that death was part of the curse for Adam's sin, then you believe that Paul was wrong about the need for Christ to overcome death. Paul, then, might be wrong about other things concerning Christ, like salvation.
This, in their mind, strikes at the very foundation of their faith. Therefore, belief in evolution is disbelief in the saving power of God's Son. So, if you believe in evolution, you don't believe in their God, or at least His Son.
This explanation is a little simplistic and I believe their are more Bible references that I could have used to more clearly provide the logical connections.
This, of course, presupposes that the "death" referred to by Paul is death of the body and not death of the soul. Confusing since many fundamentalists say the "on that day you will die" warning to Adam meant that his soul would die on that day not his body (since it didn't).
Soul, sole, Sol...pick one.