A simply way to explain this is an analogy I give my students about two lovers Jonny and Mary who live across the river from each other. During the summer the river does not flow and the river is 10 m wide. Jonny swims at 2m per second so it takes him 5 secs to swim across in a straight line.
During winter rains the river flows and when Jonny swims across he does not swim in a straight line due the river flowing but he still swims at 2m per second . His rate is the same but only the angle is affected . The river flowing only affects his angle he swims across the river.
That's why angle is affected by wind not the rate of climb/ descent .
And so the story goes...