Chazal (Vayikra Rabba 24:6) tell us that the אשה השונמית said to her husband (Malachim 2, 4:27) הנה הוא קדוש אלוקים איש כי ידעתי נא, "Behold now I know that he [Elisha] is a holy man of G-d." How did she know this? Reb Ayvun says that he never looked at her, all of his days." Chazal say about this, "Whoever guards himself from arayos is called kadosh, holy." We are discovering that everything depends on guarding the eyes. If one guards his eyes, he is holy.
It states (Bereishis 33:5) ה ַנָּשִׁים אֶת וַיַּרְא עֵינָיו אֶת וַיִּשָּׂא א ֱלֹק ִים ח ָנַן ֶׁראֲש ה ַיְל ָדִים וַיֹּאמַר לָּ ךְ א ֵלֶּה מִי וַיֹּאמֶר ה ַיְל ָדִים וְאֶת ָע ַבְדֶּך אֶת, "[Eisav] lifted his eyes and saw the women and the children, and he said, 'Who are these to you?' And [Yaakov] said, 'The children with whom Hashem has favored your servant.'" From examining this pasuk, we understand that when Eisav asked לָּ ךְ א ֵלֶּה מִי, "Who are these to you?" he was inquiring about the women and the children. Yaakov pretended that he didn't realize that Eisav was asking about the women, as well, and he answered him solely regarding the children, ָע ַבְדֶּך אֶת א ֱלֹק ִים ח ָנַן ֶׁראֲש ה ַיְל ָדִים. Shach al HaTorah explains that Yaakov was cautious not to cause embarrassment to his brother. So, he answered him as though he thought Eisav asked solely about the children.
We learn from the above that even for Eisav, it would be an embarrassment and disgrace if he weren't cautious with his eyes.