Face it, thanks to the internet anyone can waste lots of time and get worked up over things that don't really matter to them. Arsenal can win whatever they want and still have detractors, those are just having louder voices atm because of our repeated inability to win any prizes that they care about.
The detractors follow a simple flowchart:
"You haven't won anything for x years! And you call yourself a 'big' club?!"
(you win a trophy)
"You haven't won the league for x years! And you call yourself a 'big' club?!"
(you win the league)
"You haven't won the Champions League! And you call yourself the biggest club?!"
(you win the Champions League)
"You haven't won it more times than us!"
(but by the time you do, the detractors are all dead or the CL becomes so irrelevant that nobody cares if you win it)