Why this (and only this) moment is the exclusive possibility to see things as they really are?
From the Diamond Sutra, Chapter 18, speaking to Subhūti, the Buddha imparts,
...I know the mind of every sentient being in all the host of universes, regardless of any modes of thought, conceptions or tendencies. For all modes, conceptions and tendencies of thought are not mind. And yet they are called 'mind'. Why? It is impossible to retain a past thought, to seize a future thought, and even to hold onto a present thought.
This insight connects directly to clinging and attachment, which in turn, connects to dukkha (suffering; dissatisfaction with the way things are, were, or will be).
From Samyutta Nikaya LVI 11 (translations vary),
The First Noble Truth with its three aspects is: "There is suffering, dukkha. Dukkha should be understood. Dukkha has been understood."
Loosely, the Pali word, dukkha, means "incapable of satisfying" or "not able to bear or withstand anything": always changing, incapable of truly fulfilling us or making us happy.
This is a very skilful teaching because it is expressed in a simple formula which is easy to remember, and it also applies to everything that you can possibly experience or do or think concerning the past, the present or the future.
The past is a construct of a clinging mind attached to what was. The future is a clinging construct of mind attached to fantastic possibility. The present moment is all that is real and actionable.
Put another way, one can not act in the past or future. One can only act in the now (present). Attempting to act in a past or future moment ("coulda", "woulda", "shoulda") is not Samma (to slightly abuse pali) -- meaning 'not proper', 'not whole', 'not thorough', 'not integral', 'not complete' and/or 'not perfect.' And thus, out of step with the Eight-Fold Path.