I want the so to handle the end of day routine for the kid
Why can you not help out?
It's more efficient if he handles it.
If you are raising a child together, you should also help with the end of day routine. Taking care of a child is a lot of work, it will be easier on both of you if you do it together.
I don't do anything now so why would I want to do more?
Parenting is difficult and you both need to contribute. The household will work better if you do.