There's good reason to presume carbon is required. Carbon has some nice, and totally unique properties that allow it to facilitate life.

The most important features to carbon in this context are:

1. Stable catenation of atoms. Carbon atoms can bond to other carbon atoms in a long chain, and that chain does not become appreciably more reactive. This allows for the construction of very large molecules with specialized mechanical functions.

2. Ability to form stable multiple bonds. Carbon can form single, double, or triple bonds with itself (and oxygen and nitrogen), which allows carbon-based molecules to have ridgid shapes. Double bonds are found all over the place in life because they allow molecules to have sections that aren't just wiggly noodles of atoms.

3. Bond stabilities that fall in a kind of "goldilocks zone" where carbon bonds to other atoms are strong enough to resist falling apart, but weak enough to be broken later.

4. Nearly identical electronegativity to hydrogen. Carbon pulls on the electrons in its bonds about the same amount as hydrogen. This allows it to make stable bonds that are non-polar, which, when used in conjuction with other, more electronegative atoms (particularly oxygen and phosphorus) allow Carbon-containing molecules to be hydrophobic, hydrophilic, or both simultaneously. This property is what allows for complex structures like Lipid bilayers and proteins to be formed.

No other atom, not even silicon, has this set of properties, and it's very hard to imagine how you would make all but the most simplistic verson of life without these.