|I find that code reviews are a vital part of the SDLC. Having another developer review your code is incredibly useful. Developers are human beings, and as such, we can make mistakes or require room for improvement in the work we perform. How many times have you looked at some code and thought "Why did they implement it that way when this way is more more efficient / elegant / conforming to coding stadards" (select as appropriate).
Here's a useful article on what to look for in a code review[^]
If you are introducing code reviews, then you need to ensure that includes everyone - yes even the senior developers who perform code reviews need to have their code reviewed too.
Code reviews increase code quality and ensure coding standards are maintained to name just a few of their benefits.
My biggest question however is why are you having to justify their use in the first place? Anyone who has worked as a software developer in a professional capacity will understand and appreciate their benefits without requiring any persuasion.
"There are two ways of constructing a software design: One way is to make it so simple that there are obviously no deficiencies, and the other way is to make it so complicated that there are no obvious deficiencies. The first method is far more difficult." - C.A.R. Hoare