I now understand tailwind reduces the airspeed of an aircraft and consequently reduce lift. But why do the airline pilots try to fly with the jetstream? Which one do pilots prefer for the same thrust provided by the engine, a higher groundspeed (tailwind) or a higher airspeed (headwind)?
For purposes of increasing range or decreasing time to destination, one would prefer a high groundspeed. Therefore flight with a tailwind is the preferred mode.
Note that you cannot choose to have a higher airspeed for the same power setting in steady-state flight - when you encounter a transient wind condition the airspeed will momentarily rise, but then the increased drag will eventually slow the aircraft back to the trimmed airspeed.
You really need to completely divorce thinking about range/distance type steady state conditions, which is when headwind or tailwind matters - where groundspeed is to be maximised if possible - and short term transient conditions, which is what wind SHEAR is about, and where the important thing is not to have excessive and unsafe variations in airspeed.
There's nothing unsafe about 100kts of tailwind, or of headwind, in cruise; it just gets you there faster or slower. But even a 20kt SHEAR can be bad news.