They're supposed to,but it's not always true. It's mainly just an adage. It's my observation (maybe other people of observed it, too) that it seems to depend on just how much, or how they're opposite. And that some times, for opposites to be together 24/7 is difficult for the one whose opposite.

Here's a good analogy: two people walking across our great country.
On a particular day, they are on the same road at the same time, and they meet. Perhaps there is an attraction, or some reason for them to start talking to each other: perhaps one stumbles and one catches?
Regardless, they begin to talk and relate. What happened next?
Perhaps one comes from NYC, and one comes from Baltimore, but they are on the same road going to California. They are excited that they are going to same place. They talk, enjoy the time together for a while. Then one begins to see that the man is talking slower, the woman faster.
“Are you willing to walk faster?”
“No, this is the way I walk, I will not change my pace. Can you walk slower?”
“No, I want to get there sooner”
So, they part.
Another couple meet, also both from different places, also going to California. This time, they are at a very similar pace, and they both agree to change cadence a little to continue to walk together. When they get to California, one says,
“I can’t wait till we get to San Francisco, I will show you so much and we will have a great time.”
“Wait…I’m not going to San Fran, I’m going to Los Angeles, and I know we will have a great time there! “
If they are willing to explore each others destinations, or agree on a common destination, then they have a match. Of not, they will again part.
But the couple that meets and can negotiate a common cadence, and having had this experience before, right away discusses their destination and what they are willing to do at the destination; this is a winning combination. Even though they come from different places, perhaps had different gaits and maybe even different beliefs, it is the commitment to a common goal and destination that matters.

Opposites are traveling in different directions almost never get to talk to each other. If chance stops them both in the same place, and they perhaps they will spend a little time together in the middle, have a great time, and then resume their opposite courses.