The Bible's internal consistency & external consistency with real life convinced me it is God's word.  Why don't unbelievers see it?

Either Hedonism or lack of perception. 

The Scottish theologian James Orr put it like this, over 100 years ago - and it still holds true: "The subject is taken hold of by its wrong end, when the test of inspiration is sought primarily in minute inerrancy in external details, as those of geography, or chronology, or of physical science. Inspiration does not create the materials of its record: it works upon them... The Scripture fulfils the ends for which it was given ; no higher proof of its inspiration can be demanded."

But those who really don't like even the very idea of God, let alone that He has a written record that is inspired of the Holy Spirit, will nit-pick every little thing they can in the Bible, bolstering their view that they are justified, while God is not. They will be judged accordingly, by the Righteous Judge of all the Earth.

Those who love God and respect His written word to not see inconsitencies in it.

Because they think differently. 

The Bible has multiple contradictions and has been changed numerous times over the centuries. There are many helpful lessons and teachings, especially those in the Gospels, but the entire Bible should not be seen as infallible or historically accurate.  

They don't want to see.

None so blind as those who choose to be blind.

You apparently went in as a believer with a desire or profound need to convince yourself of God.

The Bibles and the Quran were all political works seeking validity for the leaders.  They existed in Theocratic societies     The study of history will make one an atheist...  

“The best cure for Christianity is to actually read the Bible.”

-----Mark Twain

"The gods offer no rewards for intellect. There was never one yet that showed any interest in it"..---- Mark Twain

Inconsistencies comparing the Bible's promises to real life observations:

1.  Prayers result in the same statistical outcomes as not praying at all.

2.  No events ever occur that cannot be explained without God.

3.  God supposedly interacted with ancient people in ways that could have been measured and recorded, then all of a sudden he stops when we have the capability to measure & record.

Internal inconsistencies:

1.  Prophecy fails.  The Psalms are generic statements that no one would ever think refer to Jesus without assuming it first.  The gospel writers forced the texts to fit the story.  The supposed virgin prophecy is not about a virgin.  Zechariah refers to 1 animal but Matthew misunderstood despite "God's inspiration" and thought it meant 2. 

2.  Editorial fatigue, where authors copying prior writings started changing details but failed to maintain the new details to the end of the story. 

3.  Stories grew and changed over time like fiction, not like fact.

Is that enough or do you want more?  I've got more!

I think it's because they don't want to see it. We have free will and, we all believe as we will. We choose to believe or not.

I read the Bible without blinders on.  There is absolutely no consistency, either internal or external outside of the handful of examples preachers point to in order to pretend that it's perfectly consistent.

Satan knows the Bible better than most Christians do. Just knowing the Bible doesn't make someone a child of God.

Ego makes the heart hard as stone. It's pride that separates people from the love of God. What do you think Jesus is knocking on, anyway?