You, and many others, seem to have the inability to realise that for Liverpool to improve, it makes **** all sense letting your best player leave, especially to the side that you're aiming to displace
Suarez may want CL football and be happy to settle with Arsenal for a year but unfortunately for him (and you), it's not his decision

You seem to be struggling with that fact.
You will quite consistently find the best clubs in the world let MANY of their best players go. To get into the top four more often than not your business has to be a success more than the team has to.
Chelsea sold Hasselbank, Robben, Gallas, Anelka, Drogba, etc, etc, etc. Real have sold hundreds of top players. Barca have sold only recently, Eto'o, Ibra, Villa. The BEST teams in the world constantly sell their best players because they do what makes the best financial sense.
Spurs have consistently improved in recent seasons by selling their best players for good prices and bringing in usually good deals and strengthed overall as a team. The clubs that hang on to their biggest financial prizes till they are worth next to nothing are the ones who never improve. Yes you sold Torres before he got crap but the team had already declined.
You've got to reinvest the money wisely and realistically Torres was Benitez's last good buy and before he went downhill. They got second but he'd wasted loads of money on Keane(not because he couldn't get use out of Keane just decided to bench him and get the worst out of him) pushed Alonso out the door in favour of.... Barry(he tried and was the reason Alonso went the following season). Replaced Alonso the the next year with Johnson and Aquaman, Maxi, the great greek lump.
I probably shouldn't point out the 6th you got with Hodgson in for half a season was the best season you've had since 08/09
Part of being a successful football club IS indeed selling your best players, for their peak value, then finding other players not at their peak, and making those guys more valuable.
Arsenal's most successful period was selling the likes of Petit and Overmars for Pires and Lauren. We played our best football when we had fairly high turnover of players and when we were doing absolutely fantastic business off the pitch. Arsenal are currently desperate, no other team is remotely willing to think about Suarez at that kind of price because he is in actual fact not worth anywhere near that. 12 pretty good months out of 30, in which he played every minute in every loss, wasted chance after chance, got a huge ban for woeful behaviour on the pitch.... AGAIN.
What has happened since he joined, 6th the year he joined, 7th since.... wow, massive improvement from him for sure. Then there is selling a player that hasn't helped you get to 4th nor best Arsenal, to a team that could spend 40mil on a different player who could make them better.
This is all ignoring that Suarez players the opposite way to Arsenal, some teams have wingers who provide balls to the focal point upfront to get all the goals. Arsenal have wingers who (particularly Walcott) need the ball held up by the striker to bring the wingers into it as they run into the box to shoot when given the chance.
He's the polar opposite of the type of striker we need and wasting 40mil + on Suarez when we could actually get the type of player we need would hurt Arsenal, not help.