why would ultrarights kill kennedy, wouldn’t they love him?

Biggest reason, based on what I’ve read, is likely because after the Cuban Missile Crises he generally favored rapprochement with the Soviet Union, which would have included the US withdrawing from Vietnam. He also supposedly had a number of spats with the CIA before this, including over the assassination of Patrice Lumumba, the assassination of Ngo Dinh Diem, the Bay of Pigs invasion, and probably much more.

He also fired Allen Dulles, the CIA director, and privately said he wanted "to splinter the CIA in a thousand pieces and scatter it to the winds." He was also sleeping with the ex-wife of a CIA agent reported to be involved int the plot, so maybe that also didn’t help things. She was murdered suspiciously in 1964 in a crime that was never solved.

So, there were quite a few reasons why they’d want him dead. The CIA at that time would not hesitate to kill a democratically elected leader who stood in their way. Why would they not apply that to the US itself?