EMB-505 pilot reported an auto pressurization fail and calibrated airspeed message and stopped the climb at 4000 feet. The crew decided to return back to the departure airport.

Narrative

On takeoff from ZZZ had an auto pressurization fail CAS (Calibrated Airspeed) message. We stopped the climb at four thousand feet. ATC wanted to continue to climb us prior to us being able to complete the QRH. They were told that we would not be climbing and that we needed to maintain four thousand; for the time being. We ran the QRH; and subsequently through our decision in the aircraft and talking with the company decided that the best option would be to return to ZZZ. We informed the owners; informed ATC; canceled the request; burned off fuel; and landed at ZZZ with no other irregularities.Suggestions:If the aircraft has a pressurization issue where you are operating the system in any sort of revisionary mode; there should be no comment made from the company in any way shape or form in regards to continuing the flight to it's intended destination. This presents a situation where you are relying on a procedure that is not only not practiced; but not even taught. (Referring to operating the aircraft in a manual mode) setting the cabin altitude to its desired setting according to the table in the QRH. This after a stressful situation and possibly at the end of a long duty day. This opens the possibility for un-necessary risk to the passengers and crew members.If this issue occurs bellow the flight levels the aircraft should land at a suitable location within 50 miles of it's position. Continuation of the flight in the flight levels should only be considered or allowed if over water or if landing within 50 miles would result in significant risk to the crew or aircraft.