Why are angels NOT visible to human,

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

The angels are made by Allaah The Almighty invisible to mankind for great wisdoms, one of which, as mentioned by the scholars, is that humans do not have the ability to see angels because they are created from light which no man is able to look at. In his commentary on the following Quranic verse (which means): {And if We had made him an angel, We would have made him [appear as] a man, and We would have covered them with that in which they cover themselves}[Quran 6:9], Ibn Katheer said: “It is reported from Ibn ‘Abbaas that he said, commenting on Allaah's Saying (which means): {And if We had made him an angel, We would have made him [appear as] a man}: “Were an angel to be sent to them, he would have come to them only in the form of a man, because they could not look at the angels, because of the light (from which they are created).”

Another wisdom may be that Allaah tests His slaves by asking them to believe in the angels who are, for them, a part of the unseen.

There may be further wisdoms we do not know of. Truly, it is Allaah Who is the Wise, the Well-Acquainted. For further information, see Fataawa 21084 and 86490.

Allaah Knows best.