Praise be to Allah.
There is a mistake in the question concerning the hadeeth and verse mentioned, which we must point out before answering the question.
With regard to the hadeeth, it makes no mention of ‘Aa’ishah (may Allaah be pleased with her), and moreover it is not saheeh.
It was narrated from Umm Salamah that she was with the Messenger of Allaah (peace and blessings of Allaah be upon him) and Maymoonah. She said: Whilst we were with him, Ibn Umm Maktoom came to him and entered upon him. This was after we had been commanded to observe hijab. So the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Observe hijab before him.” I said: “O Messenger of Allaah, is he not a bind man who cannot see us or recognize us?” The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Are you blind? Do you not see him?”
Narrated by al-Tirmidhi, 2778; Abu Dawood, 4112.
The isnaad of this hadeeth includes Nabhaan the freed slave of Umm Salamah, who is majhool. It was classed as da’eef by al-Albaani in Irwa’ al-Ghaleel, 1806.
With regard to the verse mentioned in the question, the questioner has mixed up two verses:
The first is (interpretation of the meaning):
“O Prophet! Tell your wives and your daughters and the women of the believers to draw their cloaks (veils) all over their bodies (i.e. screen themselves completely except the eyes or one eye to see the way). That will be better, that they should be known (as free respectable women) so as not to be annoyed. And Allaah is Ever Oft‑Forgiving, Most Merciful”
and the second is (interpretation of the meaning):
“Tell the believing men to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts). That is purer for them. Verily, Allaah is All‑Aware of what they do.
31. And tell the believing women to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts)”
With regard to a woman looking a man who is not her mahram, we have already stated in the answer to question no. 49038that it is permissible subject to the condition that there are no feelings of desire or any risk of fitnah (temptation).
The fact that a man’s ‘awrah is from the navel to the knee does not mean that it is permissible for a man to show his chest in front of other men, let alone in front of women. Although the chest is not part of the ‘awrah, uncovering it is still an action that is not appropriate for a man and is one of the actions of the immoral.
It should be noted that if doing something permissible will result in some evil, then it is not allowed, because of the evil to which it leads. If a man’s uncovering his chest will be a cause of fitnah or will open the door to evil, then it should be disallowed for that reason.
Clothing is prescribed for a number of reasons, such as: it is in accordance with the fitrah (sound natural inclinations of man); adornment; protection from heat and cold; and concealing the ‘awrah from the gaze of others.
When Allaah reminded His slaves of the blessing He bestowed upon them by creating clothing that covers them, He also drew attention to another kind of clothing which is better than that, namely the clothing or raiment of taqwa (piety, righteousness).
Allaah says (interpretation of the meaning):
“O Children of Adam! We have bestowed raiment upon you to cover yourselves (screen your private parts) and as an adornment; and the raiment of righteousness, that is better. Such are among the Ayaat (proofs, evidences, verses, lessons, signs, revelations, etc.) of Allaah, that they may remember (i.e. leave falsehood and follow truth).
27. O Children of Adam! Let not Shaytaan (Satan) deceive you, as he got your parents [Adam and Hawwaa’ (Eve)] out of Paradise, stripping them of their raiments, to show them their private parts”
Shaykh ‘Abd al-Rahmaan al-Sa’di (may Allaah have mercy on him) said:
Then He reminded them of the blessing that He had bestowed by making it easy for them to obtain clothing that is essential, and clothing that is worn for the purpose of beauty. The same applies to all things, food, drink, means of transportation, spouses, and so on. Allaah has made it easy for His slaves to obtain what is necessary, and what is complementary to that, and He tells them that this is not something that is be sought in and of itself, rather Allaah sent it down to help them to worship and obey Him. Hence He says, “and the raiment of righteousness, that is better” than physical garments, for the garment of righteousness remains with a person and does not wear out. This refers to beauty of the heart and soul.
With regard to outward clothing, its purpose is sometimes to conceal the outward ‘awrah and sometimes to adorn the wearer, and it serves no other purpose than these two.
Not having something to means that a man is going to leave his ‘awrah exposed, which is allowable in cases of necessity, but if a person does not have the garment of righteousness then this will cause his inner ‘awrah to be exposed, which will lead to disgrace and humiliation.
The phrase “Such are among the Ayaat (proofs, evidences, verses, lessons, signs, revelations, etc.) of Allaah, that they may remember” means this is mentioned to you about clothing so that you may remember thereby that which benefits you and that which harms you, and you may seek the help of outward clothes to help you to acquire the garment of righteousness.
Tafseer al-Sa’di, p. 248.
And Allaah knows best.