「什麼邏輯」is a phrase, commonly used to complain about the nonsense that someone is saying. The English equivalent is precisely “nonsense”.
When a harsh wife is complaining to her husband that she cannot have a successful career because her husband didn’t clean thier house regularly, hence the bad luck, her husband may use the phrase 「什麼邏輯」.
Wife：最衰都係你，一日都唔收拾下間屋，污糟邋遢咁，累到我無得升職加人工。（ I will not be promoted and have my salary increased. It is all on you, because you have never cleaned our house.)
Husband: 你呢啲什麼邏輯？你有無得升職加人工同我有無做家務有咩關係？ (Nonsense. How on earth is it even possible that because I didn’t do the chores, you get no promotions and salary increase. )