The text on this card may be a bit unclear at first, but it really is as broken as it sounds. Argent Braggart really does "gain Attack and Health to match the highest [card] on the battlefield."
For example, if there is a 1/5 minion on board and a 5/1 minion, then Argent Braggart becomes a 5/5 minion for just 2 mana. Now imagine both of those stats on a higher level.
Of course, it can still be silenced, but that' true of any strong card in Hearthstone, which has never stopped anyone from playing them.