There is a kind of wisdom that is good, and a kind of wisdom that is bad. We should acquire the good kind of wisdom, and God will destroy the bad kind of wisdom. There is simply no contradiction at all here.
Some argue that the Bible is contradictory concerning whether we should acquire wisdom or not. Here are the relevant verses:
Proverbs 4:7- The beginning of wisdom is this: Get wisdom, and whatever you get, get insight.
1 Corinthians 1:19- For it is written, “I will destroy the wisdom of the wise, and the discernment of the discerning I will thwart.”
The solution is simple. The wisdom that we should acquire, or get, is different from the kind of wisdom that God will destroy.
The kind of wisdom we should acquire is wisdom that comes from studying the Bible. The more we learn about what the Bible truly teaches about God, ourselves, and the world, the more wise we will become, and this is a good thing.
The "wisdom" that 1 Corinthians 1:19
People who try to argue against or rebel against the Bible will find that they are being irrational, and God will not only reveal their irrationality, but He will also punish them for not worshipping Him as they ought.
Some people have trouble accepting possible explanations to alleged contradictions in the Bible, especially ones that they consider a stretch. For example, Dan Barker, president of the Freedom From Religion Foundation, says this:
I have received numerous replies from Christians who think that these contradictions are either trivial or easily explained. Yet not a single "explanation" has been convincing.
The fact is that there are plausible explanations for every alleged contradiction in the Bible. That there is a plausible explanation for an alleged contradiction does not mean that it is definitely the correct explanation for the alleged contradiction.
However, as long as a possible explanation has been suggested, then it has been objectively demonstrated that there is no necessary contradiction regarding the Bible verses and passages brought up.
When people like Dan Barker say that they don't find a particular explanation for a contradiction "convincing," then that is merely their opinion. A plausible explanation has been suggested that eliminates the necessary alleged contradiction. They simply don't like it, which is not at all a relevant argument against the explanation.
To read more about solutions to Bible contradictions and difficulties, check out Norman Geisler's The Big Book of Bible Difficulties: Clear and Concise Answers from Genesis to Revelation. While we do not agree with some of Geisler's theology, particularly concerning his view of predestination, this book is still an excellent resource. It is thorough and filled with research.
Another book to check out is Tim Chaffey's Demolishing Supposed Bible Contradictions: Exploring Forty Alleged Contraditions, which also answers many alleged contradictions in the Bible.