I love the whole "universal numbers" that govern the heavens and the earth aspect of Fibs. I also like Murrey Math for the same reason. They are interesting concepts to think about and in some ways connect one to the greater whole. Trading, however, is a different story.
My main problem with Fibs was when to apply them. I will give a brief tale (example):
Price is in an up trend for last 10 periods. On period 11 price closes down. I ask myself, " Is this the start of the retrenchment? One down period does not a retrenchment make." The next period, price again closes lower. Now two periods down is obviously more than one, but are we in a pull back ? The 2 period pull back doesn't seem like much at this point. So right now, I will wait to see what happens. Now this is the kicker. On the next period, price trades down then closes on its high and higher than previous period. I read in a blog, or hear an analyst on CNBC say, that price in this market retraced 38% intra period and closed higher as all the people watching that key level entered. I thought I was one of them, but I never got to put the FIbs on. Looking back at the chart it becomes clear. I call my broker for a price fill some time in the past, and they hang up on me.
Maybe it's just me, but things like that are one reason why I don't use Fibs. When I did use indicators, you can believe they all had periods of some length like 3,5,8,13,21,34,55,89..... .......... or Music Math numbers like 8,16,32,64. Dynamic support/resistance levels like those of Market Profile came to my rescue.