"Meitim" means "dead ones" (that is, it is a plural noun, not an adjective; the singular is "meit"). And someone, something cannot be dead if it was not previously alive.

I once saw a shirt in a tee-shirt shop in Boulder, Colorado (a college town) that said "Death and Taxes are Just Unsolved Engineering Problems." Taxes I don't know about. Death is pretty dependable.

A rock is not dead; a piece of metal is not dead; sand is not dead. None of these things (and so many others) ever had life within them. It may be that the detritus from former living things are part of petroleum or coal, but the objects themselves were never alive. They are, instead, abiotic. They cannot be animated.

But to the living, death is both inevitable and more powerful than any other force in our world. Everything that comes into life is eventually terminated by death. It would make sense to seek to appease death, or to ascribe to it dominion over our lives. (Indeed, some traditions have done so.)

We affirm that God is more powerful than death. That is, God brings us into life and will, when death has taken life away, restore life to us. We can speculate on why death exists at all, but from a Jewish perspective it seems to be so dominant in our lives in order to demonstrate the superior power of the Holy One. God can rescue us from death. In fact, God gives life to the dead.

The phrase that combines "m'chayyei" and "meitim" appears with frequency over the course of the second paragraph of the Amidah. It is meant to emphasize the power of God to resurrect the dead – not just one individual, but all of us. (Another topic of speculation is exactly how and when that happens.)

Once we have established the God of our history in the first paragraph, we establish the God of our future in the second. The ancestors we remember and yearn to know better will attend the mysterious reunion that awaits us in God's time.