TL;DR: Because it's wrong. And it's opposed to Scripture.
First off, we need to get our terminology straight. Most if not all Christians don't oppose "evolution", although many prefer the term "natural selection". Organisms change over time; the evidence for this is pretty incontrovertible (just look at breeds of dogs, or of any other domesticated animal). Most people that oppose "evolution" actually oppose Common Descent, or the idea that all organisms are descended from one or a few common ancestors. (Abiogenesis, or the idea that life began from non-life without help, is also contentious.)
With that out of the way... a number of non-Christians oppose Common Descent and Abiogenesis. The Discovery Institute in particular is dedicated to this point of view, and the major reasons are that there are significant scientific problems with Abiogenesis and Common Descent, even setting aside theological considerations.
In short, there are mountains and mountains (and some literal mountains) of evidence that Abiogenesis is impossible, that Common Descent is (at best) severely flawed, and that the age of Earth and the entire universe is rightly measured in some thousands of years. (Not tens of thousands, not millions, and certainly not billions.)
As to why Christians, specifically, oppose Common Descent, let's start with some of the points in your Question:
I understand it is written in the Bible that God created humans. It isn't written, how exactly.
This isn't entirely correct. "The Lord God formed the man of dust from the ground and breathed into his nostrils the breath of life." (Genesis 2:7) The idea that humans are 'created from dust' is repeated multiple times in Scripture, and many Christians see this verse as fairly literal, suggesting that Adam was created in a manner not unlike someone forming a statue from clay. (The likening of God to a potter is also Scriptural.)
The case gets even more explicit when we get to Eve. "The Lord God caused a deep sleep to fall upon the man, and while he slept took one of his ribs and closed up its place with flesh. And the rib that the Lord God had taken from the man he made into a woman and brought her to the man." (Genesis 2:21-22)
It needs to be noted, however, that humans are special. This in an of itself is an objection to Common Descent, but the more immediate point is to compare how non-human life was created. For example, "God said, 'Let the earth bring forth living creatures according to their kinds—livestock and creeping things and beasts of the earth according to their kinds.' And it was so." God Spoke, and it happened; not in millions of years, but immediately. The image of God's Word having immediate and omnipotent power is found throughout Scripture.
What's wrong with the concept that God created the Universe in a way that 13.7 billion years later?
"In six days the Lord made heaven and earth, the sea, and all that is in them." (Exodus 20:11) Scripture is clear that Creation happened in "six days". Genealogies and other texts make it clear that the Genesis narrative starts circa 4,000 BC. Scripture consistently refers to the Flood as a real, historical event... as do hundreds of other accounts from cultures all across the globe. Peter even goes so far as to call out those who deny the Flood. "They deliberately overlook this fact, that the heavens existed long ago, and the earth was formed out of water and through water by the word of God, and that by means of these the world that then existed was deluged with water and perished." (2 Peter 3:5-6)
Scripture, read without trying to impose outside ideas on it (exegesis, not eisegesis) clearly teaches Fiat Creation and thousands of years; the ideas of Common Descent and billions of years are nowhere to be found. Not only that, the Creation narrative specifically conflicts with the Materialist narrative on multiple points.
The original idea of "deep time" is based on the idea of "Uniformitarianism", which has been thoroughly discredited. It is upheld primarily on the basis of radiometric "dating", which is full of assumptions, conflicts, and even suppressed results. Simply put, it is not a viable idea... except for those with a vested interest in keeping God out of the picture. Unfortunately, it has been played up enough (and the issues downplayed) that many people believe the fairy tale in spite of its shortcomings.
Seemingly random evolution still follows the laws of nature - what's wrong with this view?
This is the least objectionable point, but it's still problematic, because it reduces God to an entity that is bound by nature. In effect, it elevates "nature" above God.
God is above nature. God Created natural law, and God is not bound by natural law. It's true that God usually works in a regular, predictable way, but He also steps outside these rules on occasion. We call those occasions "miracles", and Scripture documents many. Water turned to wine. Humans healed or even resurrected. The week of Creation.
When we insist that God must interact according to natural law, we deny God's sovereignty. More importantly from the standpoint of a search for truth, we exclude a category of causal possibilities. Such an approach to science is artificially constraining itself to potentially produce answers that are not merely "wrong", but catastrophically so.
...And I still haven't even started on why Common Descent destroys the core of Christian theology. Humans being a "recent addition" to history makes Christ a liar. Death before humans (in particular, before the Fall) trivializes the consequences of Sin and makes God a liar when He declares His Creation "very good". (Note that "very good" here means something quite different from "great"; the denotation is rather one of supreme perfection.) Belief in Common Descent and billions of years undermines the trustworthiness of Scripture.
Common Descent is also bad for society. It is inherently and necessarily racist. It is inherently opposed to morality and sanctity of life. If incorrect, it is even harmful to scientific research, especially medical research. The reasons to oppose it are myriad, and not limited to Christian beliefs.
