First Officer reported a breakdown in Crew Resource Management led to a cabin altitude exceedance and an immediate descent to minimize the possible affects of hypoxia on the crew.

Narrative

Due to the auto side of the pressurization being inoperative on Aircraft X; the pressurization was being controlled in MAN DC by myself for all flights; including on my legs. During the flight from ZZZ to ZZZ1 approximately 35 minutes into the flight; the Captain elected to climb at Max Rate starting at approximately 12;000 feet; in which the aircraft was climbing at a rate of approximately 3;000 feet a minute. However; the manual pressurization was only climbing at 1;000 feet minute; which in turn the cabin altitude started to rise from 8;000 feet. I suggested to the Captain two times to lower the vertical speed due to the cabin altitude climbing. As it approached 9;000 feet in cabin altitude; approximately at 18;000 feet; I was directive on notifying the Captain for the third time that the cabin altitude was leaving 9;000 feet and we needed to slow down our vertical speed before we get a Cabin Altitude Warning light. Approximately at 20;000 feet we received the Cabin Altitude Warning light. I notified the Captain at that time the cabin altitude was approaching 11;000 feet and climbing; and suggested we descend as soon as possible using the QRH. The attitude from the Captain towards the event was a carefree attitude. He notified Center; and descended at 2;000 feet a minute. I initiated the QRH; donned on my oxygen mask and started going through the QRH. The Captain elected to not put on his oxygen mask; and also elected to not have the Passenger Oxygen initiated with flight attendants on board. It took approximately 5 minutes to get at or below 10;000 feet. An attendance call was made; in which a Flight Attendant replied they were okay in the back. We continued to ZZZ1; however after landing; one Flight Attendant recalled having symptoms of hypoxia (light headedness; dizziness; fatigue; and dehydration).My recommendation to my company due to my experience with working on pressurization on aircraft in the military; was to make sure the Flight Attendants and rest of the aircrew were okay; the aircraft pressurization to be fixed; and lastly to not fly with the Captain. I do believe this situation could have been avoided and/or mitigated in a better manner. Due to the lack of care and attitude of the situation which resulted in a CRM breakdown; and the lack of care of the rest of the Aircrew's well being which put their lives at risk.