I don't know why posters are saying you can't do everything for the dog yourself.
I live on my own so there is literally no one else to do anything for my dog.
I chose her, paid for her, trained her, take care of all insurance, vet fees and so on and so on.
However, that was my choice and I didn't have to worry about anyone else's wants or needs.
The fact is that if you have a dog in the house it will impact to some extent on everyone else in the house.
Yes, you can do everything for the dog, but dogs require more than just things being done for them and being paid for. They tie you down, massively. And they can be very stressful.
You won't be able to just up and go away for the weekend, or even overnight, everything has to be booked and planned ahead and unless you have someone to look after the dog while you're away you have to factor the cost of kennels into holidays.
Even going out for the day has to be planned. Even an adult dog can't be left alone for long periods, especially if you have a dog with separation anxiety. And a small puppy certainly can't be left.
And puppies may look cute but they can be really hard to deal with sometimes. Just house training can take many months with some dogs.
I can understand, if your DCs are about to leave home and you're going to have more freedom, why your DH doesn't want to tie you both down to what is effectively having another baby in the house.