Ours are the best of friends
I think it is just the youthful thing they do. The first week or so we brought Chloe our Cav home, our cat Salwa was not that amused and Chloe kept on chasing her. Now they are best of friends, they sleep together when Chloe is not busy licking the cat's ears, neck and the backside! As for the cat, as she is lots older I think she tolerates Chloe and has adopted the Cav as a little sister, or even perhaps a daughter of her own and nudges Chloe frequently with her nose. When we are busy doing stuff in the kitchen or just watching TV, we noticed they the two either play with each other or just sit next to each other sunbathing. A couple of times I got home early from work I saw them both on the outdoor table, about an inch apart, just looking so bliss. Needless to say, when they are not napping, they go look for each other I'd say every ten minutes or so. Chloe is now just so slightly bigger than Salwa. As for chasing planes,birds etc, that's just how they are wired. Just having fun.