Of all the of the Justice League, no two heroes are more at odds with one another than Green Lantern. Why do they seem to despise one another so much? Much of it has to do with their methods of seeking justice being pretty diametrically opposed as well as their personalities. Even so, is there a deeper level of respect?
It should be noted that Batman seems to really not like Hal Jordan specifically. Sure Green Lantern Guy Gardner can be obnoxious, but essentially every hero in the DC Universe finds Guy to be generally abrasive. Batman seems to have it out for Hal largely due to what seems like Hal's particular brand of arrogance and determination. Batman is a planner and a preparer, yet Hal usually dives into the fray, coming up with the solution as he goes. Green Lantern once hit the reason for the tension right on the head during the Green Lantern: Rebirth storyline from Geoff Johns where Hal Jordan broke free of Parallax's possession, becoming a hero once more. Batman met the comeback with a strong level of distrust, and fellow Lantern John Stewart had something to say about it.
Stewart goes on to say that Hal Jordan is the Man Without Fear, and what is the Batman when you're not afraid of him? Just a man, according to Stewart. That seems to sum it up pretty well: Batman uses fear and the dark, while Hal is fearless and wields light.
Johns goes on throughout his Green Lantern run, delving deeper into their tense relationship and issues, even having them trade punches. However, he also provides some more positivity, showing that that polarization can coalesce at times, forming into a respect they have for one another. Shortly after his return, forming a sort of last will and testament, he sent a message to Batman.
Do Hal and Bruce butt heads? Yes. Do they often irritate the crap out of each other? Definitely. But despite all that, at the end of the day, Batman and Green Lantern are both heroes who respect one another. They have a professional kinship with one another that is rarely spoken (except for when Hal thinks he's about to die).
