Why don't jetliners maneuver to avoid a bird strike if spotted in time?
If you're low, slow, and heavy (say, early in climb with full passenger and fuel load for a transcontinental or transoceanic leg), just dipping a wing can result in a stall and crash if you lose power while in a more than minimal bank.

The reasoning goes like this: the birds might not hit you.  If they do, it's unlikely you'll lose all engine power.  Even if you do lose all power, if the aircraft is level wings and not maneuvering, you have the most options for a safe landing (return to port, land on a nearby strip, land on flat ground or a road, etc.).

A sharp maneuver at that stage of a flight can itself cause a crash, never mind what will happen if you get a bird strike anyway.