Scenarios:

A: The bad guy is standing next to you on the sidewalk. You tell him to take a hike. He walks away at 3 miles-per-hour.

B: You and the bad guy walk side-by-side at 2 mph. You tell him to take a hike. He walks away, on the sidewalk, at foot speed 5 mph, departing your presence at 3 mph.

C: You are standing on the sidewalk and have a rotten apple in your pocket.. You toss it forward at arm speed 3 mph into the no-litter barrel.

D: You walk forward on the sidewalk at 2 mph. You toss out the rotten apple as before, at 3 mph with respect to yourself. The apple has 5 mph sidewalk speed.

For scenarios C and D, speed v = 2 mph is your walk. Speed V = 5 mph is the bad guy or the apple on the sidewalk. Speed w = 3 mph is speed of the bad guy or apple with respect to yourself.

Problem: Scenarios C and D are different physical situations.

In scenario C, bandit ground speed V = 5 mph is the mandate and relative speed w = 3 mph is the result.

In scenario D, apple toss speed w = 3 mph is the mandate and apple ground speed V = 5 is the result.

Algebra:

V = v + w

5 = 2 + 3

The algebra cannot distinguish scenarios C and D.

Here is the Velocity-Addition-Formula of Einstein-EDoMB-1905-Section §5

V = ( v + w ) / ( 1 + vw/c² )

The equation does not tell us what the physical situation is. Section §5 has, quote:

“It is worthy of remark that v and w enter into the expression for resultant velocity in a symmetircal manner.”

Unless and until we have the v-a-f as a physical situation, the quote is meaningless.