Whether you feel empathy to someone/something or not, is really quite different from whether you have moral obligations to it. I do not think I have moral obligations to a chicken, but then again, I think everyone agrees the chicken has no moral obligations to me - jokes about asshole roosters aside, I don't think you really think the rooster has wronged you by being as it is.

Maybe moral obligations can be one-way, but then only temporarily as I see it. Someone who's sleepwalking, or a baby, don't really have moral obligations to me, but they will when they wake up / grow up.