There are several reasons why Shakespeare should not be taught in high schools. Here are a few:
- It’s violent. (I defy you to find a play without some violence)
- There are mature sexual themes.
- The language is old-fashioned and difficult for kids to understand.
- Plays are meant to be performed, not read.
Sometimes it's helpful to just look around the internet and get some ideas. Here is a site with many viewpoints. Remember, this is not a credible site to use as evidence, but it's to get you thinking.
On the Pro side, you could include examples of how Shakespeare can be reimagined. Here is an article about Shakespeare taught with technology.
Here is an enotes discussion on whether or not Shakespeare is relevant today.
Here is another debate about why it should not be taught in schools.