Damian Wayne does not swim for fun.

Of course, the Manor has a pool. Damian sort of looks at the pool similarly to how he looks at the gym: it exists for practical reasons, namely training. If he really thinks about it he can acknowledge that at most such homes a pool would exist for fun, but he just isn't the sort for leisure swimming. He cannot really picture his father leisure swimming either. In fact, the pool doesn't actually get used very often in general? But it is there.

And the thing is, the weather has been very hot. Damian has not been inclined to complain about it - not like Jason, who won't shut up about it. Weather is weather. Heat happens. But he can't deny it has begun to get... uncomfortable. And the Manor has a pool.

So he's not asked you to swim for fun, see. Swimming is good full-body exercise, and one that can be done despite the oppressive heat. And there is some argument to be made that the children of the house and their friends using the pool during the summer months helps with cover and projecting the picture of a 'normal civilian life' and all that. Damian is sure that his father's positive reaction to his request to the two of you using the pool was due to that (and not due to Damian actually asking to hang out with a friend like a normal kid, surely).

Whatever the case, permission had been granted, so now here you two were, heading together out to the Manor swimming pool. To exercise. Of course.