As much as I'd love him to stay at Liverpool, I'm struggling to see the "he's a good manager" argument, in all honesty. Last season very much seemed like the exception, rather than the rule.
Started his career at Watford, taking over a team that had finished in the Championship play-offs the season before from 21st at the time of taking over (November) to er...22nd by the end of January. Then, given that they didn't sign anyone, it appears the team that finished 6th the year before remembered they weren't quite shit enough to get relegated and managed a comfortable mid-table finish.
Following his "success" at keeping almost-promoted-the-year-before Watford up, he took the Reading seat after Steve Coppell's departure. Recently relegated from the Premier League, Reading were hardly looking likely contenders for relegation. But Brentan had other ideas, steering the side to 21st by mid-December. They finished 9th after he left.
Swansea, who missed out on the play-offs by a single point the season before Rodgers' arrival, hired Brentan to continue their charge up the English league system. Guided by Brentan, who was praised for implementing an eerily similar style of play to predecessor, Roberto Martinez (Paulo Sousa doesn't count), Swansea managed to secure a place in the play-offs, and subsequently winning a place in the Premier League. Swansea then continued playing the Brendan-Rodgers-and-definitely-not-Roberto-Martinez influenced style of passing football, and managed a respectable 11th placed finish in their first season in the top flight.
As Swansea didn't quite match his ambition, Brentan then moved North, to the sunbeds of Liverpool. A team still in transition after 20 years and 7 managers since their last league win, Rodgers, #8, was going to be the man to complete their transition. New owners, money to spend, new ambition, a tried and tested (and definitely not commonplace) style of football - things were looking up for Liverpool. After a couple of season of mid-table mediocrity that had seen the previous three managers sacked, Brendan led Liverpool to 7th, one place higher than they'd finished the year before.
All was not lost though because Brendan was still in a job, and he'd come up with a new style of football that involved going shit or bust for an hour and hoping you'd scored enough for your inevitable end of game collapse to not matter. This saw Liverpool finish an unprecedented 2nd, narrowly missing out on the title after teams realised not giving them space and/or scoring 3 in the last half hour at Selhurst Park were ample tactics to halt the Liverpool charge. With the fans furiously denying that their bolt from the blue title charge was at all related to a lack of European football, Luis Suarez being one of the best players in the world, Daniel Sturridge miraculously not being injured every game, David Moyes existing, Chelsea and City also getting new managers, Spurs sacking theirs part way through the season and replacing him with a PE teacher, and Arsenal being Arsenal, it was clear that Liverpool were ready for a second stab at the long awaited 19th title.
There was a twist in the tale, with Liverpool's star man, the racist rat-face with rabies, Luis Suarez, was leaving for Barcelona. Liverpool weren't a one man team though, and in the 5 transfer windows leading up to the 2014-15 season, Brentan had spent over £200 million bringing in a squad of average wingers and strikers to cope with the departure. It turns out that overpaying for a couple of shite defenders and a crap keeper doesn't solve defensive woes though, and Liverpool now find themselves languishing in 10th, 2 points ahead of Stoke, and that team from Birmingham that didn't score for an entire month.