The mishnah in Gittin daf צ amud א (last daf) lists different positions rabbis hold about when a man can/should divorce his wife. Beit Shammai seems to be the most restrictive and says only if the guy found in her a דבר ערוה. Beit Hillel is less restrictive and accepts something even less severe such as אפילו הקדיחה תבשילו. Finally, R' Akiva takes the most lenient approach and says even אפילו מצא אחרת נאה הימנה.
According to Rashi on daf צ amud ב dibbur hamatchil אם שנואה היא לפני המקום שלח (see in that very comment the other girsa that he accepts) why didn't he say that R' Akiva's opinion is also in line with that quoted pasuk since R' Akiva's reason to allow a get is the most lenient among the rabbis for the husband since it allows something even more minor like him finding a prettier woman and that is more of a reason why he should be considered שנוי before H"?