Brahma creates. Shiva destroys. Brahma is not worshipped. Shiva is worshipped. This is because Brahma creates Kama, Yama and Tripura, desire, death and the three worlds. Shiva is Kamantaka, Yamantaka and Tripurantaka, destroyer of desire, death and the three worlds.
Humans desire life, fear death, and construct three worlds because humans fear death more than any other living creature on Earth. Our fear is greater because we can imagine. We imagine what happens after death, we imagine a world without death, we imagine a world without us and wonder what is the point of life. Unable to make sense of things, we try to control life - we get attached to things, we resist change, and we create property. Human civilization is thus rooted in fear. Its a delusion. Brahmanda or culture is Maya.
The first people who brought the word Maya into English were 18th century scholars who lived when Europe was in the throes of the scientific revolution. They used the word Illusion to translate the word Maya and the word Destroyer to describe Shiva. Since Hindu's describe the world as Maya and worship Shiva, Europeans concluded that Hindus were a people who held worldly life in disdain. This romantic, exotic, world-denying perception of India in general and Hinduism in particular still persists as tourist brochures are full of images of the Kumbhamela at Allahabad, where naked mendicants smeared with ash and holding tridents just like Shiva, line up to bathe at the confluence of the Ganga and Yamuna every twelve years.
The European gaze was assumed to be scientific, objective, free of bias and hence modern. However in the 1970s, scholars realized that Modern thought was actually not as logical and free of bias as it was claimed to be; it was informed by cultural prejudices. The translations of European scholars were clearly based on the one-life framework. Since the God of the Bible is described as creator and hence worthy of worship, they were bewildered as to why Hindus worshipped Shiva, not Brahma, a conundrum that still persiste in Modern academia. This was postmodern thinking. Hindu ideas need to be seen in the Hindu context, not using the one-life framework of Europeans, but the rebirth framework of Indians. When this is done, a more appropriate translation of Maya is Construction. Shiva then does not destroy; he deconstructs!
The word construction emerged as part of the post-modern vocabulary; it was not part of the modern (or rather pre postmodern) vocabulary of the 18th century. Thus 18th century scholars were ill-equipped to explain Indian thoughts.
Construction means a perception of the world shaped by a measuring scale that depends on cultural norms and personal prejudices. This perception changes every time there is a change in cultural norms and / or personal prejudices. What is considered right or good or beautiful today may not be considered so, all sensory inputs remaining the same. Thus the perception can be de-constructed and re-constructed. The word Illusion came from typical scientific arrogance that logic can decipher the truth free of all bias. The word Construction admits that all understanding is rooted in bias.
For Hindus Maya is a Constructed Reality. More accurately, Maya is the measuring scale that values and devalues all things in Prakriti, and by doing so gives rise to Brahmanda, an individuals perception of the world. Its neither a bad thing nor is it a good thing. It is just the way the human mind perceives reality. Animals do not live in Maya, because they do not possess imagination. Human beings do. Humans are therefore subject to Maya.
The intention of tapasya is to reflect on and deconstruct and be liberated from it. Tapa or spiritual fire burns maya and destroys Brahmanda. Shiva, the Lord of Tapasvins, is therefore the destroyer of maya. Maya nurtures Aham, the Ego, that imagines itself to be master of the world. Shiva destroys Aham so that Atma or soul can be realized. When this happens, human life is validated. Pashu, or animal, becomes Purusha.