I'm in the Benitez camp on this matter, I believe he's a better tactical manager and has a better vision of where the club should be going in the long-term than Houllier had. That being said, things aren't all rosy, and I aren't one of those die-hard fanatics either, who back him blindly.
Benitez has his faults, as do all managers, but I believe that in the (relatively) short period of time he's been at the club the squad has improved. People quickly point to his less successful signings, but at the end of the day he brought us Torres and Mascherano, two players who could literally get into any side in the world. And in my opinion, the team as a whole has a higher level of quality throughout, which reflects in our results. We are consistently finishing high in the EPL, and reaching the closing stages of the Champions League.
I do think the majority of his popularity comes from the victory in Istanbul, but he reached another final, and a semi-final. We believe we can win it every year, and it is this renewed belief that he has brought to the fans that makes him so close to our hearts. We are a force again, to be feared, which is exactly what we should be.
There is room for improvement, however. For example, Benitez arrived at the club when four English teams were able to qualify for the Champion's League, making it "easier" for him to do so. That being said, the fourth qualifying spot was based on the high level of competition in the Premier League, but as we were one of the biggest clubs anyway, I still think this was an advantage for him. Perhaps Houllier would have done better if "his" Liverpool could have qualified from fourth spot, but as we weren't reaching the final stages of the UEFA Cup every season under him, I think it's fair to say our CL progress would have been similar: turbulent and unreliable.
He hasn't won the Premiership yet, but I don't think it's a reason to fire him. I do understand it's more complicated than that - as JD has highlighted, if our season goes tits-up and Rafa has signed a new, long contract, things would look different. However, the consistency (season by season, in all competitions) convinces me that despite his flaws and occassional strange tactics, Benitez is the best manager we could have at the moment and deserves to stay.
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