Why was Edward given scissors instead of hands?

Edward started as a machine with scissors for hands.

You see The Inventor, Edward's "father", look over at one his assembly line machines almost shaped like a human, and using scissor-like tools.

As you say, over the course of an unspecified amount of time, the Inventor transforms this machine into a "human" piece by piece (for instance, in one scene you can see Edward sitting upright, waiting for his legs to be attached), all the while teaching him how to be human.

The Inventor replaced Edward with prosthetic human parts piece by piece based on what he thought was the most important feature at the time. It is clear the most important piece for his "son" was the heart, so he began with that.

Then the face was added (socially, being the most important part of a human), and I would assume the other body parts followed a logical progression due to necessity, or perhaps even just availability of parts.

The hands were simply the final piece left to make him "complete", but alas, The Inventor's untimely death left Edward stuck with the scissors he had used while he was still a machine.

All images from Eclectric Dragonfly Screen Caps Database, copyright held by Twentieth Century Fox.

Edward Scissorhands was a creation of Tim Burton's that dated back to doodles from high school. From an article about an exhibit of Burton's drawings:

One of Tim Burton’s most famous characters, Edward Scissorhands, is way older than you think. “It was an idea from when I was a teenager,” says the director of Beetlejuice ... “It had been in my mind for a long time.” ...Those and other doodles (like the self-inflating cephalopod from 1994, below) are on display at the Museum of Modern Art through April...To unearth some of the forgotten gems, Burton sifted through boxes of old drawings he’d had shipped from a warehouse in the States to his home in England. “It helps ground you and gets you to remember what interested you to begin with,” Burton says. “I’ve never really felt like a writer. It was always a visual thing for me.”

Johnny Depp says that it wasn’t until he saw Burton’s sketches that he understood who he was to play. “I instantly fell for the character — he made his way into my body.”

So, the character came first, the story second! According to Wikipedia, Edward was unfinished when the inventor died. Presumably, functioning hands would have been very difficult to build, so the sicssorhands are just very early prototypes.

Arts: Explore Origins of Tim Burton’s Goofy Gothic, By Sonia Zjawinski, Wired Dec 2009