Air carrier Captain reported a miscommunication with ATL Tower over runway exit and taxi instructions resulted in an aircraft attempting to land behind them having to go around.

Narrative

This all started as we slowed to exit 27L at N2 at landing at ATL. There was an other carrier aircraft landing on same runway behind us. That aircraft had been behind us; with [priority handling]; the entire arrival. Note that it all happened simultaneously which leads to the confusion. When we started the right turn to exit on N2 we had an aircraft on parallel Taxiway N; just to our right that could be a conflict. So; we had this aircraft in mind just before we were going to exit runway. We also had Aircraft Y on final; 27L; behind us; but we did not get any situational awareness from Tower how far. Just as our aircraft started a right turn toward N2 to come off Runway 27L centerline; Tower immediately said - in; as we perceived it; a somewhat urgent tone - to hold short of Papa at Runway 27. It was a quick transmission; and we didn't catch if it was L or R. We knew Papa was ahead of us down the runway but wasn't sure why they'd say that. We did have the conflicting aircraft off to our right which we could have cleared if we knew they were stopping; but it was close. We discussed in the cockpit for a moment and decided the safest course of action was to avoid potential taxiway conflict and steer our aircraft back left to exit at Papa. Our ground path was essentially a right turn off centerline then back to centerline. ATC immediately got angry at us and had thought we exited runway; which wasn't true. This resulted in Aircraft Y having to go around. We weren't happy in our cockpit about what had just transpired nor were ATL Tower controllers. We maintained our professionalism. The Tower controllers were predictably not happy about this either and they made that apparent on the radio in which I would frame in an unprofessional manner. An additional note was that the ATIS was reporting LAHSO operations in effect which for that runway LAHSO is holding short of Taxiway Papa. We didn't get cleared to land with LAHSO; but it did add to compounding confusion. Also note that my FO (First Officer) and I had not been to ATL consistently and were not as proficient with these 'localisms' as other carrier would be. I'd also add that with most airports - actually this was a two-day trip and we landed at six different airports - at every airport except ATL; they were directive when exiting runway or did not interrupt the exit process with nonspecific comm. I understand this wasn't the best outcome for anyone. We apologize for that. We can agree to disagree with Tower controllers; but I would recommend being more directive initially. Although we started our turn; we did not exit the runway as Tower mentioned on the frequency. I understand this was a stressful situation. As a pilot I consider ATC controller's tone; timing of transmission; and initial guidance when listening to instructions that are incomplete or when localisms are used such as in ATL. This reasoning process all happens in a split second and the factors we as a crew used to determine the correct course of action in that about two-second conversation was the fact that a directive tone was used right at the moment; we started our turn along with factor traffic to our right. We had to fill in the gaps not hearing any phraseology that had 'exit high speed' or 'join November'. This combined with the traffic meant that we were going to prioritize our own aircraft safety above all else. I don't understand why FAA allows these localisms in the sense of safety. Regardless since we were not told to exit the high speed or the high-speed taxiway; with the compounding factor of the aircraft to our right on taxiway; we had to infer what controller meant. We aren't other carrier and don't frequent ATL so this factor should be considered. We were trying to do our best to infer what the controller wanted and were at a very quick decision point. We made the wrong decision in the controller's eyes. I'm not happy with that. I'd also point out that there is a reason non-other carrier airlines don't like ATL. It's the fact of how we were treated in the phone call and on radio. We appreciate the controlling mentioning that this was not a pilot deviation; we agree. But the background chatter in the Tower was unprofessional. Also; the person I spoke to at the Tower was professional yet seemed to have issues with some of my explanations.I've deployed to combat half a dozen times and protected our US and allied troops from the air using both kinetic and non-kinetic capabilities. This has all been done safely in some challenging conditions. I attribute this to our standardized communication and debrief of lessons learned. I've listed below a few things that could have been done differently. But I think ATL controllers need to standardize their phraseology in accordance with the FAA standards. One example is this one where aircraft need instructions to be clear and concise. In this case I needed 'exit N2; N then the Papa hold short I can see how controllers may scoff this; but I think abbreviated instructions lead to 'creep' that creates a culture of cutting out taxiways. For example; the instructions to taxi to Runway 26L via Foxtrot confused my FO - versus the correct terminology of Foxtrot; Echo. Yet another example of a localism that leads to an easier job for the controllers but an 'inference' job for the pilots. Not to mention "Dixie" taxiway as a localism. What could have been improved. We could have stopped/slowed and clarified. Tower could have used differed phraseology ' Company right next high speed; N; hold short of 27R at P; aircraft on N will give way" or "Company right on high speed; Aircraft Y one mile final' ATC could have given Aircraft Y priority or closer runway to their gate which would have been 26L. Aircraft Y had actually requested 27R; but ATC gave them no priority. Spacing could have been increased for Aircraft Y. ATL needs to STOP the localisms. As well as some other East Coast airports. They are going to cause a serious accident with not following standard ATC policies and procedures."