In the end of Batman Forever Batman said to Edward:
I had to save them both, I'm both Bruce Wayne and Batman. Not because I have to be, now because I choose to be.
What meaning does it all have: saving both, choice to be and why did he say "NOW"?
By definition, this can only be an opinion rather than an “official” answer.
Riddler and Two-face had just presented Batman with an impossible choice - they had dropped both Dr Chase Meridian and Robin, with the anticipation that Batman would only be able to rescue one of them - he would not be able to “save both” of them.
Think of what those two characters meant to Bruce Wayne/Batman :
Chase Meridian was his love interest of course - but more than that, she was his grounding to his humanity, his link to being the “normal” person of Bruce Wayne.
Robin was his colleague as being Batman - so represented his deep personal core for justice.
So the effect of the choice (which do you rescue?) that Riddler and Two-face were forcing on him was that he would have to choose which facet of his character - of HIMSELF - was more important. Bruce Wayne with Humanity, or Batman with Justice. Cant have both was what Riddler and Two-face wanted.
Except Batman did save both.
I’m so doing, he proved to them - and more importantly to himself NOW - that these two sides of him, the two characters of Bruce Wayne and Batman, could not only have a forced uneasy coexistence because they had to.
Rather, his saving both Chase Meridian and Robin meant he also saved both the Bruce Wayne and Batman sides of his personality. He no longer had to choose which was more important to him since both were, and being wholeheartedly unified he is stronger for that union.
Im going on a limb here, but Batman went through a transition because he tried and failed to save Robin's parents. He had always felt like being Batman was something he had to be. But, watching Robin go through the same, without being consumed by his alter ego, showed Bruce Wayne that it is possible to be both and to finally let go of the trauma that his parents death had caused him.