Please please go ahead with the planned neutering.
There are so many yorkies out there needing homes already and your little man really doesnt need to meet a lady yorkie to have a fulfilled life!!
As you say, your brother is being a 'typical man' not feeling comfortable about neutering! They are comparing a mans feelings with a dogs, and they really aren't the same...lol.
As your little boy is booked in with the vet already, it must be what you want to do deep down inside.
