It’s the age old question that’s caused many a debate but we’ve never had a conclusive decision so it still needs to be had.
It sounds cheesy but it is a mixed bag, as while similarities in philosophies and goals are important, if two people have the same character traits or are both type A personalities, then there will probably be more arguments than agreement.
People who say it does speak from the perspective that we are at times drawn to what we do not see in ourselves. So an introverted individual may be attracted to someone who is outgoing and personable.
Nobody wants someone who is exactly like them because then that would not only be predictable, it would be downright boring.
However, it cannot be a carte blanche statement as some opposites just will not work. People with opposing religious beliefs such as agnostic and fundamental Christians will clash, and clash heavily. This is because at the core of it all, the differences are probably too deep or too wide to just say kiss and make up. A little difference is intriguing, and may even add spice to a relationship, but when they are clearly divisive then you may spend all of your time, outing fundamental fires instead of fanning sexual flames.
Sometimes the things that initially attract you can eventually be the thing that annoys you the most. For example, you like a man who is passionate and not afraid to speak his mind right? Well later on when he becomes your man this can become annoying because now it comes across as being very opinionated and someone who always have to have the final say on everything.
Couples who are believed to be opposites may not necessarily have more fights or conflicts than others. People view differences in terms of food, styles, if you sleep in or are a morning person and what you do for hobbies. While these do not necessarily match up, other things factor in as well such as values, beliefs, how you express yourself, love languages and communication style and if most of these align, you can overlook what you do not agree on and focus on what you do.