The Mishna in Gittin 9:10 provides a few different interpretations of ערות דבר (Deuteronomy 24:1). While the school of Shammai hold that for a man to divorce his wife he needs to find significant fault with her (דבר ערוה - possibly a crime of licentiousness), it is the opinion of the school of Hillel that he may divorce her if she only burnt his food. Rabbi Akiva's opinion, which is the most permissive of the three, is that he may even divorce her if he found another women whom he prefers. The language of the mishna in question is as follows:
בית שמאי אומרים לא יגרש אדם את אשתו אלא אם כן מצא בה דבר ערוה שנאמר כי מצא בה ערות דבר ובית הלל אומרים אפילו הקדיחה תבשילו שנאמר כי מצא בה ערות דבר רבי עקיבא אומר אפילו מצא אחרת נאה הינמה שנאמר והיה אם לא תמצא חן בעיניו
The school of Shammai say: A man may not divorce his wife unless he finds in her a matter of lewdness, as it says, "If he finds in her an unseemly thing" (Deuteronomy 24:1), but the school of Hillel say: Even if she burnt his food, as it says, "If he finds in her an unseemly thing". Rabbi Akiva says: Even if he found one more beautiful than she, as it says, "If she should not find favour in his eyes" (ibid.)
I have heard it said that the reason for the permissiveness of Rabbi Akiva and the school of Hillel is that if we interpret the passage as do the school of Shammai then every woman who is divorced by her husband will be suspected of adultery. By technically allowing divorce to occur for trivial matters, we preserve the dignity of Jewish women who, once divorced, may be suspected of having done nothing more heinous than burn their husbands' food - or of being guilty of nothing more than being married to a womaniser.
I am trying to find the source for that particular chiddush, which I think is very clever. To my mind, it sounds fairly late - maybe 19th/20th century - and I don't know how to go about finding it. If anybody has heard it before and can provide me with a source, I would very much appreciate it.