There is exactly a 1/4 left turn ( from backing DC to Facing DW , lady in watlz, quick step .) in progressive chasse to Right . Why is it not called progressive chasse to left ?

Yichin 1. Where did you dig this one up. From the man's position the Quarter Turn goes to the left moving sideways. There is a quarter of a turn to the right starting diagonal to the wall within the four steps. Now you are facing diagnal to the wall against LOD. From her a Progresive Chasse will bring you back to facing diagonal to wall by making a quarter of a turn to the left. This is where you started. From here hold that line for a Lockstep finishing also diagonal to the wall. The Step that is called a Quarter Turn to the left is replaced by the progressive Chasse. Nobody does the Quarter Turn to the left anymore.

Maybe I skipped too much for this question.
This figure is called Progressive Casse to Right ( quickstep . lady part )
It was described as follows:
1 RF back TH backing DC start to turn L on 1 strat to rise e/o 1 NFR CBM 1 S

2 LF to side T pointing DW 1/4 between 1and 2, body less turn , continue to rise on 2 Q

3 RF closes to LF T, facing DW , slightly body turn on 3, continue to rise on 3 Q

4 LF to side and slightly fwd TH facing DW , no turn on 4, up on 4 lower e/o 4 S

Even I hit my head against the wall I found no hint toward the right nor right turn. Even the part of man , they all talked about the left turn 1/4. Help!

My question is why progressive chasse to right only has left turn.

The dancers are moving sidewards along the line of dance to the right. The sway (Tip) as you call it, is due to the amount of turn and cbm made to the left from the previous figure. Good dancers will travel a long way to the right,with flight,by pushing strongly from the standing left foot and moving from the left side rightwards. I hope this helps.