Not sure this is an argument for why you should have one but there are downsides to not having one as well...

My father and a few friends don't have middle names and all of them say they absolutely hate not having a middle name. As almost everyone has a middle name these days, they said it's really embarasssing when they're asked what their middle name is and when they say they don't have one the response is "why, couldn't your parents think of another name?"

My middle name is my nana's middle name (although she was known by her middle name) and we decided to name my daughter after her as well but used my nana's actual first name (Matilda) as my daughter's middle name. I have another friend who used her maiden name as the middle name for both her two boys (she did have a boy's name as her maiden name though).

Good luck convincing him! Would love to know how you go!!