Why does Nick choose to share his thoughts and feelings with Jordan in Chapter 3 of The Great Gatsby?

The quick answer is "because Nick and Jordan are beginning a semi-romantic relationship;" however, the tenor of your question makes it seem as if Nick spends most of Chapter 3 discussing his thoughts and feelings with Jordan, while that is not so.  In fact, most of Chapter 3 deals with the frivolity of the roaring twenties found within one of Gatsby's lavish parties.  There is one instance, however, when Nick speaks with Jordan about being "a rotten driver," that is a bit significant in regards to both of their characters.  This conversation is prefaced by this passage:

Jordan Baker instinctively avoided clever, shrewd men, and now I saw that this was because she felt safer on a plane where any divergence from a code would be thought impossible.  She was incurably dishonest. . . . It made no difference to me.  Dishonesty in a woman is a thing you never blame deeply--I was casually sorry, and then I forgot. (58)

After Jordan almost hits a workman working on the side of the road, Nick gets into the meat of the conversation with Jordan revealing, what I would imagine to be the thoughts and feelings you speak of:

"You're a rotten driver," I protested.  "Either you ought to be more careful, or you oughtn't to drive at all."

"I am careful."

"No, you're not."

"Well, other people are," she said lightly.

"What's that got to do with it?"

"They'll keep out of the way," she insisted.  "It takes two to make an accident."

"Suppose you met somebody just as careless as yourself."

"I hope I never will," she answered.  "I hate careless people, that's why I like you." 

Her gray, sun-strained eyes stared straight ahead, but she had deliberately shifted our relations, and for a moment I thought I loved her.  (59)

This small dialogue reveals a lot about these two characters.  It highlights the carelessness, dishonesty, and shallowness of Jordan while stressing the honesty and integrity of our Midwestern Nick. 

Ah, but the answer to "why" Nick reveals his thoughts and feelings here is in the last line in the above quote.  Nick is confused about his feelings for Jordan.  He is attracted to her, but something rubs him the wrong way.  Of course, this doesn't stop him from pursuing a summer fling, or at least a mild relationship.