Question

Why do some elements like carbon have different oxidation states in different elements whereas some elements like oxygen have a fixed oxidation number?

Answer 1

First, carbon is often more electronegative (2.5) than some of the atoms it’s bound to (such as H, 2.2).
Secondly, unlike metal-metal bonds, carbon-carbon bonds are ubiquitous.
Two answers.

In a C-H bond, the H is treated as if it has an oxidation state of +1. This means that every C-H bond will decrease the oxidation state of carbon by 1.
Any two bonds between the same atom do not affect the oxidation state (recall that the oxidation state of Cl in Cl-Cl (and that of H in H-H) is zero. So a carbon attached to 4 carbons has an oxidation state of zero.
So unlike metals, which are almost always in a positive oxidation state, the oxidation state of carbon can vary widely, from -4 (in CH4) to +4 (such as in CO2)