why is many to many relationships a problem in relational database design code example

Example: how to join tables with many to many relationships

SELECT 
    p.person_id, 
    p.name, 
    a.conference, 
    b.publication
FROM
    person AS p
    LEFT JOIN (SELECT
                   pc.person_id,
                   c.conference
               FROM
                   person_conference AS pc
                   INNER JOIN conference AS c 
                     ON pc.conference_id = c.conference_id) AS a
      ON p.person_id = a.person_id 
    LEFT JOIN (SELECT
                   pp.person_id,
                   ppp.publication
               FROM
                   person_publication AS pp
                   INNER JOIN publication AS ppp 
                     ON pp.publication_id = ppp.publication_id) AS b
      ON p.person_id = b.person_id