A319 Captain reported the need to apply heavy braking to avoid a collision with another aircraft that had been taxiing too quickly and without regard to other traffic.

Narrative

On taxi out we were cleared to spot X. Approaching the spot the F/O (First Officer) contacted ZZZ ground and we were given the clearance to taxi to XYR via Taxiway 1 and Taxiway 2 with clearance to cross [the crossing runway]. Still approaching spot X and Taxiway 1 both the F/O and myself noticed a VERY FAST TAXING 737 approaching from the gate ramp area heading directly towards Taxiway 1 instead of spot Y or Z that would have been assigned by ramp control. The F/O then made the comment 'I don't think he is going to stop!' to which I replied 'I don't think he is either!' Then to avoid a collision; I started breaking; HARD! Then we hear the 737 call ZZZ ground for clearance to which ground replies; '[callsign] follow the Airbus on your right......unless your going to cut him off....which I see you already have...well.... I guess go ahead and go first.....taxi to XYR via Taxiway 1 and Taxiway 2 cross [the crossing runway]. Aircraft Y replies with a disingenuous 'sorry'.In my opinion and observations the Captain of Aircraft Y was taxing aggressively; recklessly; and carelessly to intentionally 'beat us' to Taxiway 1. He didn't have clearance from ground; never slowed down; and made no effort to take ownership of his mistake. Aircraft Y was on their last leg of their trip and was obviously 'pushing' to get home to their base. I waited a day to sleep on the events before reaching out to the ZZZ1 Chief Pilots office on how to proceed. His recommendation was to go through professional standards first; which I did. The results were not encouraging or corrective from the offending Captain. He didn't take ownership of his dangerous actions or feel he did anything wrong even in light of ground admonishing him for cutting us off and his FO responding with 'sorry'. Professional standards described the Captain as 'difficult'. Had this Captain made a poor judgment mistake in his rush to 'beat us in getting home' and showed remorse either at the time of the incident or later when contacted by professional standards; I would have let this go hopefully knowing that this Captain wouldn't do it again to someone else. Unfortunately that does not seem to be the case. I strongly believe this Captain needs to be disciplined on the safe operation of the aircraft and not play 'chicken with jets' on the ramp creating collision hazards.