I can "kinda" see what they intend here, but that's not what support here means. Yes, they're the backline damage and aren't supposed to initiate fights on their own (especially if they cannot win). He definitely did not have a clue about the whole dashing thing, his argument would have been stronger if he had said that they don't have abilities to strongly initiate fights or something.
But in reality, if you ask me, technically everyone supports in a team by providing one aspect they're strong in, and the others cover their weakness. The tank supports by soaking damage/applying cc or dps, the mage/assassin eliminates and nukes the adc/apc if possible, the adc supplies constant dps and eliminates the enemy frontline, the support protects the adc and the rest of the team if possible, and the fifth member provides whatever role is necessary.
Every part of the team is necessary, and by that I view everyone as "supporting" each other rather than outright "carrying."
Though your friend is pretty much wrong. He might have something to argue about, but he needs to strengthen his argument and do his research before making another case if he wants to be taken seriously.