Why is light invisible? Why can't we see light? The thing which makes everything visible is itself invisible. Why is it so?
 A: The other question is sort of a duplicate but only if the OP understands why. (Or it's actually what he was asking, which I'm not sure it is.)
When you "see" something, it's because your brain is interpreting the interaction of photons with material in your eye. Your interpret more interactions as brighter and different energies as different colours. The only time you see photons, therefore, is when they travel into your eye. So if they're just going past or buzzing around, there's no reason you would see them. To see something, light must scatter off it. The way in which it does so determines how the object looks.
The other question asks about photon self-interaction. Its related because, if photons interacted with themselves, then photons would scatter photons into your eye, and you'd see them.
This may be seem like an irrelevant tangent but I hope this helped answer your question...
A: According to common usage, one doesn't see the photons reaching the eye. 
Instead we say that we see the objects who emitted them in the direction of our eyes. To some extent we also see objects in a light background if they absorb the background light.
This means that to see an object it must either be able to emit/reflect photons or absorb enough of them. Neither is the case for light itself, as (due to the linearity of the Maxwell equations) it doesn't interact with itself. (Actually there are tiny quantum corrections that lead to very weak interaction, but this is by far not enough to be easily observable.)
However we see beams of light in a dusty room, as photons scatter off the dust and so the path a beam travels is illuminated. Note that we don't say that we see a beam of dust, though strictly speaking this is what reflects the light and hence is seen.
A: I want to keep it in a simple way. Light is invisible because, there is no light striking the light (photons) and bouncing back to your eye.
A: Because Maxwell's equations are linear.  Equivalently there is no elementary photon-photon interaction.  If there were, say, a quartic photon interaction then you would be able to see a beam of light directly instead of seeing its interaction with dust particles.
A: We don't 'see' photons, we 'detect' photons. Photons are size-less and moving faster than a bullet. Believing we can 'see' something with those characteristics is illogical.
Yet, looking around me now, I see different color objects and areas which are light or dark. How am I seeing, what I can't possibly see?
The answer lies in how vision works. The process is relatively simple. Light strikes an object and is reflected towards our eyes. Our eyes detect the light and send electrochemical impulses to our brains visual cortex. Here our brain interpretation these impulses and creates a visual representation of the object, from which the light originates. We then perceive the representation. "This is the part which most people struggle to comprehend."
The concept is called 'indirect realism' and although many understand the words, they don't understand the concept. When you look around you, you are NOT seeing the outside world. You're NOT seeing reality. Your eyes DO NOT see shapes for our brain to interpret as trees, cars, dogs, etc.
Those trees, cars and dogs, ARE THE REPRESENTATIONS. Our eyes see nothing. Understanding indirect realism is the key to comprehending why we can't see photons but can see objects. The light we see is not photons. It's brightness, which is a visual sensation, resulting from the amount of photons, striking our retina.
We DO NOT SEE LIGHT. We see objects, illuminated by light. It's the objects which appear bright.
I expect this answer to be down voted as it usually is, but I'm hoping that one or two people will grasp what indirect realism truly is, and grasp the difference between 'detect' and 'see' photons.
A: Light is only electromagnetic radiation similar to what radio waves are.  Do you see radio waves? No. A radio receiver is needed to translate these waves into music, speech etc from a radio station.  In the case of light the receiver is you who is "designed" to translate the waves of light and/or photons  into what you see. 
A: This is like asking why we can't hear sound waves.  We do, that's the only thing we "hear." We merely interpret it as the sound of the things from which the pressure waves emanated.
Same with light -- we see photons (i.e., the photons striking our retina triggers neural signals), nothing more, nothing less. Our brains interpret the pattern of photons as a map of whatever emitted or reflected them before reaching our eyes.
