I am as different from an ancient Greek as I can get. Their form of democracy isn't known in today's world, their politicians had different agenda's than ours do today. Their lives revolved around their city-states in ways that I will never know, and they relied on the cycles of the agricultural year much more than I even want to comprehend.
My food comes from Walmart, I know no famine or hunger, and my table does not wax and wane according to the weather and season. I am very thankful for what I have, but I cannot comprehend the same reliance on the blessings of food that the ancient Greeks did. A festival of the first harvest for me has drastically different meanings than it did for them.
Medicine and Technology have advanced in ways that the Classical Greeks would not understand. Comforts of today empower my life in ways they could barely dream of. No horse borne buggies or lamplit nights for me. I have access to libraries from all over the world at the slightest touch of a button, and have entertainment brought into my home every minute of the day and night.
I am not Greek, we are as different as night and day. Our reasons for worshipping and ways of religious expression will only naturally be different.
Why not Reconstructionism?
My answer to why I chose Greek Wicca instead of Hellenism.