No one knows Green Lantern Hal Jordan better than his former mentor, Sinestro. The future leader of the Sinestro Corps correctly identified what Jordan's biggest failing is, which may explain their never-ending conflict.
Few rivalries are as bitter as the one between the first Earth recruit of the Green Lantern Corps and its most infamous traitor. After Hal was inducted into the cosmic organization, Sinestro took it upon himself to teach Jordan the ropes. Sinestro was quite close with Jordan's predecessor, Abin Sur, and was insistent that the person who wore his ring be up to Sinestro's standards. Hal Jordan and Sinestro eventually found begrudging respect for one another, but that respect was severely damaged when Hal's mentor betrayed the Corps and became his greatest enemy. Since then, the two have butted heads, even whenever they found themselves fighting a shared enemy. The reason Hal and Sinestro seem to always be butting heads was revealed in a candid moment during Hal's earliest days as a Lantern.
In Green Lantern #34 by Geoff Johns and Ivan Reis, Sinestro and his mentee are fighting against a rogue Atrocitus who is attempting to kill a young Black Hand and access the power of the Black Lantern Corps. Atrocitus gains the upper hand and attacks Sinestro with a yellow backhoe, exploiting the former weakness of the Green Lanterns' Power Rings. Before he can deliver a killing blow, Atrocitus is disarmed by Hal, who successfully uses his ring despite the yellow impurity. Sinestro restrains their prisoner while Jordan eagerly exclaims how he was able to overcome something no Lantern has done. Sinestro downplays Hal's accomplishment, going so far as to deny it actually happened. Hal curses out Sinestro, causing the seasoned Lantern to chew out Hal's need to "stand out".
Sinestro isn’t wrong. As a Green Lantern, Hal Jordan has often had a cocky attitude and is one to find his way to the spotlight. However, the fact that Sinestro is attacking Jordan over his need to be seen as special is pretty delicious irony. Sinestro spent years in the Corps boasting that he was "the greatest Green Lantern", so his comment comes off more as jealousy that Hal had conquered the yellow impurity before him.
More than anything else in their shared history, this moment so perfectly encapsulates why Sinestro and Hal have the relationship that they do. As with many villain and hero dynamics, Green Lantern and Sinestro have a bond over a shared trait (in this case, their desires to be number one). But two driven personalities like that are always going to come into conflict. Sinestro couldn't encourage Hal in his victory over the color yellow because it would've meant Sinestro isn't the greatest. Hal never backed down from his growth as a Lantern and in response, Sinestro eventually left the Corps to prove he could keep the universe in order better with fear. Sinestro may have pointed out Green Lantern's biggest flaw, but he accidentally revealed his own at the same time.