Many rivalries exist in My Hero Academia, and some are much healthier than others. The Midoriya-Bakugo rivalry is iconic to the series, and their Pro Hero equivalents, All Might and Endeavor, have one of their own. This is mostly a one-sided affair, with the flaming hero Endeavor being fiercely determined to dethrone All Might as the #1 Pro Hero.
The top two heroes competed for years to save lives and defeat villains. Endeavor was pretty ferocious about it, to the point he had a Quirk marriage to finally surpass All Might through one of his children. Endeavor had bitter feelings toward his frustratingly powerful rival, but it's not as clear what All Might thought of Endeavor in return.
Why All Might May Have Disliked Endeavor Professionally
MHA's Pro Heroes often keep their opinions of each other private, and All Might did the same. He rarely commented on other heroes, instead focusing on his own career and his quest to find a successor for One For All. Privately though, All Might almost certainly knew he was the subject of a fierce one-sided rivalry that bordered on obsession. He didn't seem to take this personally, but on a professional level, surely All Might realized this was unhealthy. Pro Heroes have every right to compete over the top 10 slots and push themselves to be better than the rest, but Endeavor became a twisted antihero about it and often alienated people as a result.
The generous, compassionate All Might wouldn't like that, and worst of all, Endeavor's selfish goals were in conflict with the spirit of being a Pro Hero. Crime fighters like them are supposed to put other people and society first, risking their lives to humbly shield the innocent masses from crime and natural disasters. Heroes get paid and are often idolized, but they're not meant to specifically chase fame and riches. That was why Stain the hero killer targeted so many heroes, assassinating the "phonies" who cared more about their image or wealth than the true principles of heroism.
All Might put heroism first, hence Stain's approval of him, but Endeavor's attitude is the total opposite. On a professional level, All Might almost certainly knows his rival is doing things the wrong way. No one could blame him for disapproving of this or even disliking Endeavor for being a brutal, selfish antihero who cared more about the glory of surpassing All Might than doing his job for its own sake. Ideologically, any true Pro Hero would find Endeavor repulsive, and surely All Might finds Endeavor's career choices disgusting on some level. He wouldn't say it aloud, but he must be thinking "Endeavor, you're not yet a true hero at heart."
Why All Might Could Never Hate Endeavor Personally
Professionally, All Might likely finds Endeavor's attitude and goals deeply disturbing, but he still won't allow any bad blood between them. He may be #1 and a true hero at heart, but he's too humble and selfless to boast or look down on others. When he sees a weaker or emotionally twisted person like Endeavor or Katsuki Bakugo, he doesn't see someone worthy of contempt. He sees a rogue who has lost their way and wishes to help them. All Might is an optimistic person who sees the best in others, and will never give up trying to coax it out of them. He knows Endeavor and Bakugo have the makings of true top-tier heroes, and sees their faults as obstacles to overcome.
Even if All Might found Endeavor's attitude repulsive during their one-sided rivalry, there's no way he gave up on his rival. More likely, All Might generously awaited the day when Endeavor would transform himself into a true hero, and by Season 6 of the My Hero Academia anime, that patient optimism has paid off. Endeavor is trying to atone for his past wrongs and fights hard not to prove himself, but to truly fulfill his duty.
Whatever his personal flaws, Endeavor is the true #1 hero inside and out and All Might must be proud of him. In fact, if he ever disliked his rival personally, he may now feel guilty about it in light of how far Endeavor has come. All Might would be justified in disliking Endeavor's professional goals and methods, but All Might simply cannot bring himself to hate a person -- with the possible exception of All For One, the symbol of evil. All Might has a generous heart, and it has paid off many times when other heroes would have given up. It's little wonder Midoriya looks up to him so much, and shares the same feeling about Bakugo.