If you bring home newborn chicks, they haven't adapted to any other home. You're the first one they've been in. This gives you both the ability to get used to each other right from the beginning.
They Will Get to Know You
Baby chicks are fragile, but they can also be handled with care. In fact, the more you hold them, the more they'll get used to being held. This translates into tamer, calmer adult birds. (Many chicken owners attest that their hens come running when they call for them. I have a couple chickens that love to sit on my lap, if I happen to sit down in the yard when they're out for 'recess'.)
Starting this handling at the beginning helps them get socialized to humans more easily. (As a safety precaution, always wash your hands BEFORE holding the babes--to protect them from your germs--and AFTER handling them--to protect you from their germs.)
You Will Fall In Love
Not only will they get to know you, but you will fall in love with them. The bonding experience happens when taking care of something so tiny and completely dependant on you. Of course it helps that they're cute. But it goes beyond cuteness.
If you have never had chickens before, it's interesting to watch them go from babyhood to adult, which they do at a neck breaking speed. They will change DAILY right before your eyes.
Not only are super cute, they're also entertaining. Because they have to be indoors (or in a very protected, warm environment) for the first 6-8 weeks of their little lives, you'll get to see them A LOT and spend time laughing at them.
You'll Get What You Want
If you're looking for certain breeds, or want a variety of chickens, starting from day olds will greatly increase your odds. More (in both quantity and variety) chickens are sold as chicks than as pullets or adults.
You'll Get Maximum Eggs
If you start with chicks, you will raise them into hens and be able to benefit from their best laying years. Buying an older hen may mean you've missed her most productive period of time.
What if You Still Don't Want Chicks?
To be fair, there are a few reasons people like to start with older birds and not baby chicks. Here's that list too:
Setting up a Brooder
Some people just don't want the hassle of setting up a brooder or taking care of them (inside) for the first 2 months.
Takes Too Much Time
Time translates into money, and feeding a bunch of chickens for 5-6 months before they start laying eggs is a draw back. Buying older chickens cuts down on that waiting period so you can being to see a payoff for your investment.
Fear of Loss
Some are afraid, because of the fragile nature of baby chicks, they'll die easier than if they were older. While this might be true, there's no guarentee. For instance, I've raised 20 hens from chicks and never lost any while they were young. However, I've also brought home older pullets and have lost some.
Fear of Not Knowing Enough
Baby chicks need some special care, but it's not rocket science. Anyone can learn how to raise chicks and do it successfully. Knowing the basics is a great place to start, and you can pick up the rest along the way.