Why SAT Requires A Non-determinstic Algorithm?
It is not true that it requires a non-deterministic algorithm.

You are right; if it is solvable, it should be solvable by a deterministic algorithm. And it is. This deterministic algorithm needs exponential number of steps (with respect to number of propositional variables $n$) because only known general case approach so far is to test all combinations of truth values of propositional variables, and we have $2^n$ possible combinations (rows of a truth table).

However, we can (theoretically) solve it with a non-deterministic algorithm in polynomial time which is how a class of NP problems is defined. This is where your confusion, and maybe a bad choice of words in the literature, probably comes from.



All non-deterministic algorithms can be simulated by a deterministic algorithm. In fact, all that is computable can be computed with a deterministic algorithm. It is just the time complexity that varies.