No, you don't. There is no right to be rebooked to any odd and way more expensive itinerary when SK booked you into their flights same day via PEK. If you can't accept the delay, ask to travel the previous day - or ask for a refund or book on your own if you really want to travel SG via SIN. I assume that if you were to pay for the ticket yourself you would never book a SG ticket via SIN and CPH.