Why don't you prove that they are my ancestors?
No one is going to "prove" that. It is however the very most reasonable conclusion to draw from the current evidence.
The evidence is three million years ago there were none of "us" around. There were however critters like Lucy who had some characteristics in common with us.
Since the evidence also show how we fit in very, very well with all modern life the mostest bestest conclusion is that we had someone around then as our great... great grandparents. We can judge from what evidence we do have now that some millions of years before Lucy there was nothing around that was as close to us in form.
Lucy is therefore the most reasonable candidate we have right now for a representative of those grandparents. There is absolutely nothing about her that precludes her as one. If you think there is you'll have to produce whatever it is that precludes her.
Not only do we have those characteristics that tie her to us but we have subsequent evidence that shows later forms that are closer yet to us. Since they had to have ancestors too Lucy is a good candidate to represent those ancestors. Those later forms, being yet more like us, are even better candidates to be not-quite-so-many-greats grandparents of us. Again there is nothing to preclude them from that role (and in fact less than Lucy).
Whatcha got? Anything other than you don't like the idea?
You weren't ask to prove that she is or isn't our ancestor. You were asked to show that she
could not be. Whatcha got?
Edited by NosyNed, : add a bit