I think it's professional jealousy coupled with lack of principle.
His Dark Materials books are beloved, as is he as an author, but on a vastly smaller scale to that which JKR's Harry Potter world has been. HP /JKR are revered and celebrated, to the extent that some people can't see the line between their own reality and the fantasy. I've never seen anything like that behaviour about HDM.
I wonder if resentment hasn't brewed and boiled over over the years - after all, they both emerged at a similar time in the 90s, and arguably, HDM is a much more accomplished body of work. JKR is credited as the woman who got the young reading again. PP's ego probably found that a bit galling.
Now, the same people who fantasise about being in the HP world are hurting (self inflicted, because they have believed lies about JKR, but hurting none the less) and PP is cynically rubbing salt into the wounds by continuing to insert himself into a matter he claims he doesn't understand. Perhaps he is desperately hoping JKR will suffer a massive downfall, and that the annals of literary history will hold his own books up as the definitive reading of the 1990s, with a revisionist history as to whom the resurgence of the love of reading fantasy genre novels should be attributed. Perhaps he is hoping to convert her readership and boost his own sales. Who knows? He certainly seems to have taken on the role of agent provocateur in this, as opposed to Stephen King's who just flip flopped around and ultimately didn't want to be the "bad guy".
"The Golden Compass" film flopped because it was not true to the book (and the sequels were canned). It contained none of the critique of religion that was so central to His Dark Materials. Pullman's quotations from the time of production seem to indicate he agreed with and justified all the liberties taken with the original story, including making Mrs Coulter blonde (he said at the time that it made perfect sense and Mrs C should have been blonde in the books too - yet she was back to being dark haired in the TV adaption without comment from Pullman). What principled author, allows their work of genius to be butchered so? JKR, by contrast, seems to have kept the world she created on a fairly tight leash, working on the script adaptions to keep them true to the original stories, and being determined not to lose her characters to the Hollywood machine. And she still has Hollywood at her feet begging for more. Savvy as well as principled, talented, gracious, generous, kind and funny.
JKR must boil PP's piss on a daily basis.