Normalization is a must for any halfway decent database modeling, you shouldn't throw it away that easily. Many-to-many is a relationship you can't ignore, nor does it break normalization rules by itself.I never really got why but I just did as I was told. Many to Many relationships is taught at university as wrong, having one in an assignment project would cause you to be marked down, as your database would not be fully normalised. So you'd get rid of duplicates and columns not dependant on your primary key etc etc (i hate normalisation, and promptly forgot it after my exams)
Database schema is one form for representing data, it doesn't necessarily map directly to the entities in the system (though it's usually close enough). Not every table represents an entity in the system. Using a pivot table is the normalized approach to implementing a many-to-many relationship.The pivot/junction table is the additional entity which makes the tables theoretically not many-many.
In your posts you implied that this relationship is "frowned upon" / undesired, you should be more clear in what you mean as to not mislead people who are not familiar with those terms.