Sorry, Melanos (and sorry I can't do the accent in your name), but Jack lies quite a bit.
He's still a vibrant, amazing person with lots of great qualities, but he lies. Besides the examples you list above, he also says to Ennis: "I ain't (queer) either." [Ennis didn't know what he was saying; Jack did.]
If you want to go into the short story, in the motel Ennis says somehting like, "You ever think of doing it with another man?" and Jack, who had been riding more than bulls, said, "Hell no."
To paraphrase the sagacious *tpe*, we love them with their faults. And not just in spite of their faults, but because of their faults.