Why cannot we see Angels?
Since angels are spiritual beings created out of light, they are not visible to humans in their original form and real appearance. Our eyes were not created with the ability to perceive angels. However, prophets could see angels in their real appearance because Allah gave them the ability to see angels.
That we cannot see angels in their real form and that we cannot perceive them with 5 senses do not mean that they do not exist. There are many things that our sense organs cannot perceive in the material world. Our ears cannot hear the sounds that are too low or too high. If we could see the light waves that are determined by special devices and see especially x rays and ultraviolet rays, we would know the world in a very different form than we do.
How can we deny the existence of numerous events in the endless realms that Allah Almighty created though we cannot perceive the reality of the things that we see in our own realm?
Thus, that we cannot see something with our eyes cannot be the proof for the non-existence of that thing. There are so many things that cannot be seen by our eyes that we accept their existence with our mind, science, experience and experiment. Angels are among the things whose existence we accept though we cannot see them with our eyes.