I think one interesting way to look at deconstruction is by looking at the "Sola Scriptura" doctrine of Protestant Christianity.

Most ordinary, church-going Protestants probably wouldn't even recognize the term, but it's critical to their beliefs and practices. Sola Scriptura is the original distinguishing idea between Protestants and Catholics. In essence, it says that truth about God and humanity's relationship with God has been fully revealed in the Bible. No further revelation is coming. Christians can think hard about what the Bible says but must be careful not to add to the Bible in either belief or practice.

This idea can cause a lot of conservative Christians a lot of problems. Because many of their beliefs and practices can't be "re-constructed" by studying the Bible.

Get a bunch of people together who've not been exposed to Christianity and ask them to construct a faith system based on the Bible.

Are they likely to construct teachings that it's wrong to drink alcohol, to dance, to enjoy sex, etc? Are they likely to conclude that homosexuality is always wrong? That women must be subordinate to men? That most levitical law doesn't apply to Christians, but some specific levitical laws do apply? Would they be able to construct standard Evangelical Christian end-time prophecies?

No, frankly, they would not be likely to reconstruct contemporary Christian beliefs and practices. (For example, those end-time prophecy beliefs didn't even exist until a couple hundred years ago. Nobody who didn't already know the details would be able to read the Bible and come up with them again.)

So conservative Christians who believe implicitly in Sola Scriptura, even if they don't understand the Latin phrase, can find themselves strongly motivated to deconstruct their beliefs ... once they realize the construction they've been working with has no foundation.

Catholics and progressive Christians are less likely to deconstruct in the same way, because Sola Scriptura is not meaningful for them.

(To be clear, many progressive Christians sign on to Sola Scriptura as a foundational theological doctrine, but they belong to churches that constructed beliefs and practices very differently from conservative Evangelical churches. Other mainline Protestants, like Anglicans, never adopted Sola Scriptura.)

So, what many Christians mean by deconstruct is carefully examining beliefs in light of what a plain reading of the Bible could produce without centuries of tradition being added on.

This process normally results in somewhat more liberal or progressive ideas.

But that's just one sort of deconstruction. No universal definition exists.