I don't know what you are asking.

What I think you're asking: "Why are you guys arguing about whether it's a pass or a dribble since either one is illegal?"

If that is correct, then you are right that once A1 touches the ball the play is illegal. But if it's (determined to be) a pass, then it's not illegal until it's touched by A1. If it's (determined to be) a dribble, then it *might* be illegal as soon as A1 begins the dribble. And, you *might* not be able to determine which it is until later (or maybe you can make such a determination). That's the focus of the discussion.

No "probably" about it, and also not the play we are discussing.

Well since the initial post did not state what happened before the player dropped the ball, whether he ended a dribble & jumped or he received the ball while airborne, i just though i took it into consideration on a 2nd case where no pivot has yet been established.

assuming the player established a pivot before he jumped, the player can't dribble anymore because he already lifted his pivot before releasing the ball so it'd be a travel right?

unless he merely came into contact with the ball while on the floor & yet catch/secure the ball and only manage to do it while already airborne, this case he hasn't established a pivot until he has landed, so he can actually just hold the ball until he land or "drop" the ball as a mean to start a dribble.

If the player received a pass while airborne there would have been no reason for this discussion.

well it could still be a violation if he touched his own pass. but if he dropped the ball & touches it would you see it as a violation or just treat it as a dribble?

Depends on different things, for example:

1) if he dribbled already
2) did he pick up his pivot foot before releasing the ball

No, it wouldn't.

There is no rule about "catching your own pass." there is a rule about moving your pivot foot which is what USUALLY happens. But when it doesn't ...

Why?