Brendan Rodgers, sufferer of ornithoscelidaphobia, inserted not only a release clause into Roberto Firmino's contract when he moved to Liverpool in the summer of 2015, but he and owner John Henry also decided that the clause would contain a "sorry, Arsenal, but you aren't eligible to buy Roberto Firmino" clause as well:
This, of course, stems from the infamous £40,000,001 bid Arsenal launched to activate Luis Suarez's release clause in 2013, which was blatantly rebuffed and ignored by Liverpool (while Suarez would have been a nice addition, the subsequent purchase of Mesut Ozil a month and change later probably would not have happened).
As to why Liverpool decided that this clause needed to be in the contract of Roberto Firmino, a guy who was to replace the production Raheem Sterling provided but has since failed to replicate his predecessor, remains to be seen. Having an anti-Arsenal clause in, say, Coutinho's contract makes more sense than a guy who's not performed at the level expected for a player that cost Liverpool nearly £35 million. Then again, purchasing players at inflated prices only to see their production fail to match expectations and fees is a common occurrence on the red side of Merseyside.
In any case, having a clause specifically to prevent a player moving to a specific club is the height of paranoia. It's fair to say Arsene Wenger shook John Henry, Brendan Rodgers, and all the suits at Melwood.