I always thought that was a mistake and furthered ridiculous identity revelations in Batman films. At least it's not as bad as when Alfred decided to bring Vicki Vale into the Batcave after a few dates.
I suppose we are supposed to believe that Bruce loves Rachel and takes this moment to reveal himself and cement some bond, reaching across the cold chasm of his secret identity. But I don't buy it.
The moment is contrary to Batman's character and exists only because the writer wanted to provide an arch for their relationship. It's really forced and I wish they'd found another way to develop that part of the plot.
That's apart from the fact that there was zero chemistry between Katie Holmes and Christian Bale. Thankfully, Maggie Gyllenhaal took care of that in the sequel.