Gamophobe

The fishes jump over the bridge,
soaring upstream to reach the high waters.
They catch plump flies, green,
that hover just below silver boughs
which in the sunlight do gleam,
of summer days stretched by the stream.
To eat a fish, to pin it, and boil it
and spit out the bones, makes me feel most uneasy.
Until that warm and tender flesh
that is ever so heavenly fresh.
I know and love, leaves my mouth in a haste,
headed down the line, felling full in the body and in mind.
I have not wasted time, for fish understand the likings of my kind.
For when the school swims away
there's no longer any reason to stay.

All the (Need "All"? Need "the"? I'd pick one of them to delete.) fish jump over the bridge,
soaring upstream to reach the high waters. (Delete "the.")
They catch plump flies, green, ("green" made this line stagger a little bit. If you feel that "green" is necessary, perhaps try reworking this line to fit it into the rhythm.)
that hover just below silver boughs (Great line!)
of summer days stretched tautly. (Change "tautly" to "taut." Yes- I looked it up- "stretched taut" is grammatically allowed.)
To eat a fish, to pin it, and boil it (Simple- it does wonders.)
and spit out the bones, will leave me
full in the body, but empty at heart. (That comma after "body" adds a nice pause. Good job there.)
For when the school swims away
there's no longer any reason to stay. (Meh. Seeing as you don't have rhymes for the rest of the poem, I'd contend that "stay", here used, seems forced, as if it popped into your head last second and you thought it was blindingly genius. I'd replace that word with something more concise, but that still effects your meaning.)