Break this down, though. Scope the big picture. Somewhere in the myriad of reasons, what draws you is their turn of phrase, their ability to engage you, their style...the nearly indescribable and intangible quality called voice. It's unique, theirs. And if they can develop it, so can you if you're not afraid to be yourself.
In the 1960's there was beautiful housewife who with surgical enhancement became a phenomenally gorgeous actress. Her acting ability was debatable, but her power to draw a crowd to theaters was undeniable. Her studio swathed her in an animal skin, ran the projector, and Jo Raquel Tejada Welch became America's favorite sex symbol in the mid-sixties.
At the same time, the daughter of a roguish father and over-bearing mother wrote a book that shot her to stardom. She wanted to be an actress, but it was her penchant for pulling her past experiences--and those of her friends--that made her famous. Valley of the Dolls became an international bestseller for Jacqueline Susann.
I'm not advocating you wrap yourself in leopard skin or dive headfirst into drug abuse. I'm asking you to contemplate what makes you different. Can you use that in your writing?
An attorney friend calls John Grisham a hack. I asked "Why do you keep buying his books?" He couldn't answer to his satisfaction, but I hid a smile. Grisham drew him because of his uncomplicated, easy-going style, his ability to break down legalities that are convoluted so laymen could understand them. He has a unique voice.
If none of the above makes much sense, do an exercise that may make the light bulbs go off. One phrase: You can't handle the truth.
Who do you imagine saying that? If you're a film buff, you probably thought of Jack Nicholson.
Now...same sentence...this time spoken by George Clooney. Brad Pitt. Meryl Streep. Literally dredge your memories for those actors' voices. Different inflections, right? Different timber, pace, intensity, mood.
That's voice. Each is unique, including yours. Some voices are more powerful depending upon the moment.
Recall Pitt as Achilles in "Troy", his grief then fury after Patrocius is killed in battle. Can you see anyone else playing the part?
Just as each actor polishes their skill, as singers hone their talents (another exercise...have various people perform "Mary Had A Little Lamb" for you--note the differences in delivery between Tony Bennett and Elmer Fudd or NIN and Journey), writers must define and refine themselves in order to find their voice. This ability to deliver words in a fashion that projects them onto readers' memories is in essence what establishes them separate, apart from other writers, even within their own genre.
Before you find your true, authentic voice, maybe there are obstacles you must overcome. My money is on fear being your nemesis. Often we sit to write and are stymied not by what comes next but on how we say it. VOICE. Good friend and American western historical writer Leigh Stites covers this topic extremely well in her February, 2012, president's column for Midwest Romance Authors. As she states: Fear will kill you. Fear will kill every dream you have. It will kill the momentum you need to achieve those goals you set when you weren’t so afraid. It will kill the future you might have had if you’d been brave enough to leave the cave and go out hunting.
Put on your rhino skin, because the writing world is tough. Arm yourself with your writers' tool box, and venture forth. Don't let fear stop you.