Since you didn't specify which perspective you're looking for (other than the view of skeptics, which is off-topic considering this site is meant to cover what Christian groups teach), I'm going to provide an answer from a Fundamentalist view - one that holds Scripture to be inspired, inerrant, and infallible.
Before doing so, I need to point out, however, that this site is not here to discuss which view is correct. We're here to provide answers about what is taught, and believed, not whether the teaching or belief is valid. I'm going to stick strictly to that guideline here.
Also, There are plenty of Christians that regard the Genesis account as allegory, rather than as actual recorded history. The view is that the Genesis account is along the lines of one of Aesop's fables (or maybe as one of Jesus' parables) - a fictional story with a teaching purpose. For those that hold such a view, the idea that there is an apparent discrepancy doesn't at all pose a problem. It wouldn't affect the doctrine of inspiration at all. A discrepancy here would only affect those who hold to a literal interpretation of the genesis account (A.K.A. Young-Earth Creationists). For Young-Earth Creationists, this would pose a problem.
But again, I remind you that this site is not here to debate "who's right". The answer I'm about to give is not intended to convince anyone that there is no discrepancy, that the Y.E.C. view is correct, etc. It is merely to provide the answer that would come from someone with that particular perspective.
(That's a lot of disclaimers. Sorry about that, it's often necessary on this site with this topic.)
Part 1: Is there a discrepancy?
The typical answer to this apparent discrepancy uses common Apologetic rules for resolving apparent discrepancies. Those rules are summarized on another question on this site: Rules behind resolving alleged Biblical discrepancies. These rules are designed to avoid logical fallacies, and keep both sides honest.
Summarizing the ones relevant to this question:
- In all logical arguments, the burden of proof must be on the person that is claiming that something exists.
- It's impossible to prove the non-existence of something, because you'd have to know everything. It is possible to claim that something exists because you need only find one example as proof.
- If we were discussing "Does God exist" the burden of proof would be on the Christian to prove His existence.
- In this case, the question is "does a discrepancy exist?" so the burden of proof is on the person claiming that there is a discrepancy.
- If a single plausible explanation for the discrepancy exists, then you have not proved a discrepancy. the explanation may not be personally convincing to you, but that is irrelevant. (And again, on this site, we're not here to convince you.)
- Many Biblical discrepancies are resolved by simply understanding the context of the passages. Failure to understand context of certain passages is by far the most common cause of misunderstandings.
With that, let's take a look at how CARM - an organization that meets all of the criteria for being Young-Earth creationists that hold to a literal interpretation of the genesis account, including Books one and two. On their article on this question, they list all of the apparent discrepancies, and then provide the following answer:
There is no contradiction between Genesis 1 and 2. Genesis 1 is a
detailed explanation of the six days of creation, day by day. Genesis
two is a recap and a more detailed explanation of the sixth day, the
day that Adam and Eve were made. The recap is stated in Gen. 2:4,
"This is the account of the heavens and the earth when they were
created, in the day that the Lord God made earth and heaven." Then,
Moses goes on to detail the creation of Adam and Eve as is seen in
verses 7 thru 24 of Gen. 2. Proof that it is not a creative account is
found in the fact that animals aren't even mentioned until after the
creation of Adam. Why? Probably because their purpose was designated
by Adam. They didn't need to be mentioned until after Adam was
Creation.com puts it like this (One quote out of a rather large article):
Genesis chapters 1 and 2 are not therefore separate contradictory
accounts of creation. Chapter 1 is the ‘big picture’ and Chapter 2 is
a more detailed account of the creation of Adam and Eve and day six of
Thus showing that the apparent contradiction could plausibly be simply a misunderstanding of the context, ignoring that the two accounts are given for a different purpose.
With a plausible explanation, we cannot, while remaining intellectually honest, say that a contradiction exists. No contradiction has been proven. You can find the explanation personally unsatisfying, and unconvincing, and still believe that a contradiction exists, but that is a different thing than proving a contradiction.
So at best, you can have an unsubstantiated belief that there is a contradiction here. Last time I checked, skeptics were pretty smug about not adhering to unsubstantiated beliefs.
Part 2: What is the Radical's Critics case?
The Radical Critics case is, therefore, a flawed argument based on logical fallacy and a misinterpretation of the context.
“When it is realized that there are two distinct creation stories in
Genesis belonging to two different periods and derived from two
different sources, inconsistency becomes intelligible. That it exists
at all, however, is sufficient to discredit a theory of divine
inspiration that is obviously out of accord with the facts.”
is rendered moot by the application of consistent rules of interpretation as demonstrated above, as applied to the extreme literal view of Genesis.
It's even more ignorant when you factor in the fact that many Christians believe the creation account to be allegorical with no impact on the doctrine of inerrancy. Even for fundamentals, the existence of allegory, hyperbole, and other literary devices has no impact on the doctrine of inerrancy. The arguments put forth claiming that a difference in the two accounts invalidates the inerrancy doctrine is a clear example of the straw-man logical faccacy.
All in all, the arguments hold no water and are easily shown to be ignorant, at best, or intentionally using straw-man arguments while ignoring basic logic at worst. Either way, they hold no validity when examined without the use of logical fallacy.