It made sense for all parties. Liverpool wanted Coutinho to stay 'til the end of the season and apparently played the cup-tied card with him, but Barca basically said it was now or never and so put pressure on him to agitate for a move then. I guess from Coutinho's point of view you have the World Cup coming up this summer and you have no idea who the next shiny thing (in other words the next James and Kroos!) that the big Spanish clubs will want to sign up will be.

From Barca's point of view they lost a hell of a lot of face with the Neymar debacle and so Dembele and Coutinho are statement signings to prove they still have it.

And for LFC, the choice to keep or sell was apparently given to Klopp and as you saw with him at Dortmund, he'd rather have committed players. Coutinho never really fitted into Klopp's preferred system from a positional sense, but he was such a world class game changer that the square peg had to be crammed in there somehow. Without him you see games like Man City and Porto where Liverpool are playing more efficiently with more hard workers in midfield. Klopp has also been experimenting with new formations with Coutinho gone too, we'll now regularly switch to three at the back if we're holding onto a lead. That's not to say he's not a loss - after all, he was worth disrupting the system for - but losing Firmino would be twice as bad as losing Coutinho.