Because of you're attachment to the material world. The most fundamental attachment is the idea, "I am the body", or "the body is mine"; therefore if it dies, 'I die', which is the source of the fear of death. This has been a well understood concept in the East for many thousands of years, but not widely accepted in the West, where we tend to have a superficial and materialistic view of things. It is a result of ego conditioning, which operates by and identifies with the material paradigm of form and 'content' (component, specific, details).
Humans are prone to being mistaken and misled in our judgments and observations out of the failure to recognize the formless realm of essence and 'context' (meaning, significance, implications), in favor of the material view. The nonlinear always results in the linear. How else could 'Immaculate Conception be possible? The 'emptiness' of the sky allows "clouds to pass" freely. 'Sound and motion' are the ever-present background that makes "sound and motion" detectable. It is out of 'intangible and formless' thought that ideas arise as tangible form.
This is not only confirmed spiritually, but also scientifically. All physical matter and energy is completely made of nonphysical subatomic particles that never physically interact with each other. The opening passages of The Book of Genesis do not explain the "beginning of existence", as the Presence of God would signify that existence, 'already exists'. What the Bible is describing is the 'origins of form', saying that God made the "heavens and earth" from the 'formlessness' of "darkness and void", before He said, "Let there be light".
The world of material form is transitory and not meant to last, hence, nearly every major religion is founded on the spiritual principle that this life is meant to be used to prepare us for the next; whether it's another earthly incarnation or an eternal afterlife. Seeking material and worldly acquisition is futile, and inevitably results in suffering. "Claiming ownership" automatically brings up fear, because we all secretly know that what can be "gained" can "lost".
God is the 'Ultimate Context' to go by, because there are no limitations He can be subject to. An 'Unlimited God' is not bound by the restrictions of a 'this' and 'that', 'here' and 'there', 'now' and 'then'. Because of man's identification with material form, we tend to project our own limitations upon God, and depict a distorted view of faith. This is how people cannot understand how an 'Omnipresent and Omnipotent' God can manifest Himself in the flesh as, 'Divinity Incarnate'.
Jesus could not say, "I am God", because Divinity is without ego to do so. Anyone with ego can "claim" to be God. Why would an Omnipresent and Omniscient Being have to address 'Himself' as Himself, 'to Himself'? When Moses asked God, "Who shall I tell them sent me?", God did not say, "It is I, God!"; but replies, "I am that which I am" (some interpret, "I shall be what I shall be"). Thus, John 5:30-31, "If I testify about myself, my testimony will not be valid. But there is another who testifies about me, and I know his testimony is valid".
Christ came to make the New Covenant with humanity, because of man's material understanding of faith, and our depiction of God as "elsewhere", since Adam and Eve in the Old Testament. How is it possible to be "separate" and "apart" from and 'Omnipresent God'? The God Jesus spoke of in the New Testament is described as a 'Transcendent Reality', as well as an 'Immanent' one ("I and the Father are one", "I am in the Father, and the Father is in me").
Jesus taught that we are all God's children, and that the same 'Divine Essence' dwelling in Himself, dwells in us all ("...ye are gods", "...the Kingdom of Heaven is within you"). The Father/Creator is the aspect of Divinity that is all around us, The Son/Created is the inner Divinity within, and the Holy Spirit/Creation is Divinity that is through us. These designations are used to avoid the ego's flawed judgment of Divinity, in recognition that The Lord cannot be confined by limitations.