EMB-170 Captain reported a lack of consensus with maintenance over a cabin pressure discrepancy. The Captain refused the aircraft and swapped equipment to continue the flight.

Narrative

We flew the plane into ZZZ and noticed the pressurization was acting up as I felt it in my ears. Once on ground we received a PRESS AUTO FAULT message. Was doing IOE and had my OE complete the GRG (Ground Reset Guide) and fill out the can. The message cleared and didn't think much more about it. All boarded up and told the Flight Attendant to shut MCD (Main Cabin Door) and once the door was shut the plane pressurized. Cabin alt went to -500 ft. Had a 1;000 ft. climb rate and differential pressure was 0.3 psi. Max is .2. I called Maintenance and received some push back from the person I was talking too. I referenced the max .2 psi and his response was that's on take off and landing. With proper aircraft knowledge the plane should not pressurize with just the APU on in the auto mode. I said its not right and he responded yet again and then I finally said just send out Maintenance. Maintenance came out and immediately said its not correct as I took a video of the issue. They wanted to see it themselves so we removed the passengers and was able to duplicate the issue. The more times we duplicated the issue it got worse. After a power reset and some trouble shooting they couldn't fix it. Of the numerous times not once did a EICAS message appear. Had a plane swap and had an issue with it and had to call the Job Card Supplement about something that I can't remember and he asked me about the pressure issue on Aircraft X. Didn't think much about it but once in ZZZ1 I received an email from Job Card Supplement and it stated that Maintenance found a big piece of insulation stuffed in the out flow valve.Maintenance needs to stop being so quick to say nothing is wrong or having a quick MEL. I could have seen this as in issue as I refused to go with the issue and another Captain could have went with the push back I received from Maintenance. They act like they are personally themselves are paying for Maintenance to come out to the plane. They are worried about delays in my opinion instead of addressing the issue.