Should I give my reason for leaving in my two weeks notice letter?

No, you should not give your reason for leaving in your two weeks notice. Simply stating that you are leaving and when you will stop working (two weeks minimum from the date of the letter) is enough. Leaving behind a written record of an issue you had with the company could impact your chances for a positive recommendation for future employers. Even if you dislike a job, you should leave the company with professionalism and courtesy. If an HR representative presses you for your reason for departure during an exit interview, you can politely discuss any issues at that time if you so choose.