Why Photography is a piece of Art?

To classify Photography as a piece of art we should first understand what a piece of art is and why it's called so.
A type of visual art
What are the things we generally refer to as "piece of Art" or "matters of Art" or "Art related" or "Artistic"? Reply would include: Poetry, Novel, Music, Dance, Paintings, Sculpture, Theatre, Films and of course Photography. Among these, Poetry and Novel would be further classified as literary arts; Dance, Theatre would be classified as performing arts whereas paintings, sculpture, photography would be Visual Arts.
As art is defined as a human activity which tends to express a view or an emotion in the form of some creations what others can see, hear, touch, feel or experience through the sensory organs, Photography can be a good fit as per the definition.

The photographer wants to express his or her view or how s/he looks at the object through the photograph. In other way the photographer may simply want to highlight a scene in his or her way, the way s/he deems beautiful or important to notice as the case may be. Others can see what the photgrapher has created through his or her camera.

Difference from other types of visual art
Now the point of argument is whether this piece of art is a real creation like other piece of visual art?
What's the minute difference between a paintings, sculpture and a photograph? Well it's not hard to figure out! A photograph is a captured live scene which has happened in the past. The photographer doesn't do the work of recreating any live action. What he simply does is imprint what he or she sees on a medium. this medium is either a digital sensor or a film.
You build a sculpture or draw a painting either copying or getting inspired by what you see in your eyes. But for Photography you don't build anything; you just capture what you see in your own eyes. If you happen to create something, arrange a background only for the sake of capturing it in a frame you design a set for photography. Technically speaking its also a photograph and a piece of visual art.

Photography is a form of art which you don't create but capture
Its a confusing paradox, indeed! If a photographer is not creating anything new from the scratch how can it be called a piece of art? Well, to justify the simple reply would be: what a photographer creates is a "perspective", a way of looking at some object or an arrangement of objects; a vision what may not have existed in the eyes of the viewers. A photograph is that perspective or that vision which comes out from no where! 

Photography - peeled off

Mode of visual communication:
Photography is a medium of stationary visual communication. Its a communication because you want to communicate something to the world. Its visual because the recipients of the communication receive the content of it through their eyes only. Its something which interacts with the visual organ; gives birth to a reactive signal which casts an impression on the brain of the recipient.
It is stationary because the content doesnt change with respect to the time frame. In simple term, Its still, as if the content is snapshot of an incident which has happened in a particular point in time.

Difference from Videography:
The particular point in time is important as this is what makes Photography different from "Videography". The latter is actually a series of single photographs, taken in a continuous path of a time frame. Otherwise Videography is same as photography as far as medium of visual communication is concerned, except the audio content, if audio is captured as the same time. So to put "videography" to a comprehensive classification, it will look like this: Videography is a medium of non stationary visual communication. Videography is a close associate of photography or to put it this way, the fundamental to Videography is Photography. These two aspects of visual communication are actually refered to as "Videography" or "Motion Pictures" and "Still Photography" to avoid any confusion.

Concoction of Art, Science & Technology:
Coming back to Photography as a subject, it can be classified as a wonderful concoction of Art, Science & Technology! No other subject in the world would ever be as amazing amalgamation of the three subjects as Photography is! Let's look at it from these three subjective angles. Its a piece of art because like any other piece of art it has a content which has been created by its creator (like an Author creates a piece of poetry!) as a message for the world. It can be aesthetic to sooth the eyes of the recipient or the content can simply be a captured visual frame of something which the creator wants to communicate. By this argument, its a piece of art like poetry, a piece of drawing, a piece of pottery or a piece of critical review as well. It's a creation by a creator, called Photographer!
Its Science because its process of creating the artistic content draws on the laws of science - both physics and chemistry. The laws of optical physics work well for capturing the photograph on a photographic film or a digital sensor. Though the application of chemistry is limited in digital photography, it is fundamental in developing the negative photographic film to a visible photograph.
Its Technology because the tool we use to create the content is called Camera which is a technological innovation enabling the photo artists or the photographers create the visual content easily wherever, whenever!
To sum it up, Photography is a mode of stationary visual communication created artistically applying the laws and principles of Science, powered by a technological platform