In The Waste Land by T.S. Eliot, why does he say, "April is the cruelest month"?

According to Eliot, who wrote those famous opening lines
to his poem "The Waste Land," April is cruel because it leaves you hoping and wishing
that spring would come, but it never really follows through.  It is a time of year when
people are sick of winter and cold and want the light and warmth again, and April
usually delivers a few nice, sunny days just to tease us.  But then, the rains and the
cold come back--it is a cruel thing to do, to tease us with warmth and then be cold and
muddy again.

Later on, he uses seasonal imagery that is
reflective of April, using it to symbolize society, and how it is not fulfilling, and it
is empty.  The imagery of April, "breeding Lilacs out of the dead land," and covering
"dull roots with spring rain," indicates the potential for rebirth.  But later on, in
lines 19-24, he states that in April, there are only roots and no leaves, and that "the
sun beats, and the dead tree gives no shelter."  It is not fully spring yet, and it is
not fully still winter. So, we have empty trees and dried roots and no green, and sun
that we can't shelter from in the leafy shade.  This is all symbolic of Eliot's message
about a people that feel lost and empty, wandering, and in search of meaning.  April was
the month that he opened with to symoblize that.

I hope
that those thoughts help a bit; good luck!