Miscommunication.
If the pilot had offered 180 knots to 6 or even 7 DME the controller would have had no problem.
The controller could have also offered that because i think the BA pilot was a little too huffy to even understand the question how long he would be able to maintain 180.
ZALPO is at 6.8 DME which is 5.4 nmi from the threshold.
(
https://de.flightaware.com/resources/airport/KJFK/IAP/ILS+OR+LOC+RWY+22L/pdf)
In the approach chart you can also see another problem: DME is 1.4 nmi more than distance to the threshold.
Now the controllers mean 180 to 5 nmi from the threshold.
Saying "180 knots to 5 miles" would be unambiguous.
180 to 5 DME is a little ambiguous though.
Not sure if that ambiguity is ever a problem, but i believe it might well be sometimes.
Anyway the pilot was busy explaining why he couldn't fulfill that ("ridiculous" in his eyes) request.
The controller only wanted to know how long he could maintain 180.
Which he then replied that he was slowing to 160.
When the approach clearance was given the BA plane was "7 from ZALPO" which means on a 12 mile final.
Slowing to 160 so far out was as i said probably a misunderstanding.
They were both within their rights to do what they did though.
The pilot can slow down if he deems it necessary and the controller can resequence them to keep up efficiency.
One might argue just slowing down the plane behind BA might have been more efficient and that the controller acted out of spite.
But being uncooperative with ATC might get you going in circles, that's just how it is.