Answer by Dave Hughe:
Fibonacci lines and pivot points are in favour because they work.
Why they work that's a different question, to which there is no straight answer. But isn't that amazing to see how price touches a Fibonacci or a pivot line and reverses its course?
Personally, I use FIbonacci lines and pivots to set profit targets. On many occasions they enabled me to take profits just 1-2 pips away from the reversal point.