Another answer has already noted that you might expand the contraction if you want to emphasize one of the words in it individually. And you're right that you'd want to avoid it in the most formal writing—e.g. I would use contractions in a business letter or an opinion essay in a newspaper, but I find that I (unconsciously) avoided them in my dissertation paper.

Another reason I can think of is that you might expand the contraction simply to increase the overall emphasis. Contractions "relax" the tone; removing them makes it not only more formal but more emphatic. If you have to repeat yourself and are getting frustrated, you might expand the contraction:

"Where'd you go just now, Junior? I was looking for you."
"Mommy! Mommy! I'm hungry! I want an ice cream cone!"
"Junior, you didn't answer me: Where did you go?"

As I tried to come up with examples just now, I feel like we might be more inclined to expand the contraction the longer or more difficult to pronounce it is. A short, easy contraction like "it's" might survive even furious intensity ("I SAID it's FINE!!"), though you might expand it if you've gotten to the point that you're spacing your words out ("Listen very closely. That... is... not... okay!"). I have a very hard time imagining "can't" being expanded to "can not" in all but the most icy formality or raging fury. But "what'd," "where'd," and "why'd" seem much more eager to expand. "What'd" in particular, with its double consonant, is hard to say, and comes out sounding pretty much the same as "what did" anyway."

Finally, the expanded form can be easier to understand. If you used a contraction and someone failed to understand you, you might expand it, or you might leave them out when talking to small children, the hard of hearing, or non-fluent speakers.

Is it bad to sound formal in everyday conversations?

My general answer is "no." My spoken language is often rather academic, because I feel no shame in being a "geek," and use words like "whereas" in actual conversation. More importantly, formal forms are often clear, and when learning a language, it's better to be clearly understood and thought a bit "stiff" than to be misunderstood in an attempt to be "cool." I would always encourage learners to learn standard forms first, and adopt slang or figures of speech only as you hear them used around you.

But it is worth getting accustomed to contractions and using them comfortably, because yes, it can make you seem stiff or stilted to always avoid them, and sometimes this can cause the reader to perceive a tone that you don't intend.

On the TV show Star Trek: The Next Generation there's a humanoid robot character named Data. His artificial intelligence is human-like, and one episode even argues that he should be considered "a person" with full rights, but a running theme is his Pinocchio-like desire to be "more human," and his frequent failure to read social cues and adjust his tone to the occasion. One stylistic gimmick in the development of his character is that he doesn't use contractions. Regardless of the fictional explanations for this, it has the narrative effect of heightening his "non-humanness" and calling attention to his failure to fit in with the rest of the crew.

Avoiding contractions can make you "sound like Data." Worse, it might be mistaken for heightened emphasis or anger. And a mismatch in tone can be heightened depending on the tone that's expected for the situation. If I got a printed invitation in the mail inviting me to a dinner party, then I would think nothing of formal language. If, instead, my close friend invites me to come over for burgers and beer, and they email:

You are invited to my house. We will have burgers and beer...

... Then I might think to myself, "Geez, why so formal? You're not addressing the board of shareholders here, it's just a get-together." This is drawn from real life, in fact; I have a friend who communicates this way, and I've come to expect it from them and know it's just how they write. But at the worst, if I were new to the friendship, I might worry that I had offended them and they were angry with me. This might be even more likely if the communication were by text message!