For those who are not familiar with the terminology, a "ship" in fandom refers to a couple that you want to see together romantically. It's short for "relationship." Check mine out below, starting with my OTP ("one true pair"), whom I ship the very most. As you probably know by now, I'm a huge romantic, and I take these ships pretty darn seriously. SO DON'T ARGUE WITH ME.
They're both wonderful characters whom I adore, and Wanda is the closest thing I've ever seen to an accurate representation of myself in pop culture.
They're Avengers who fight to protect the world, they have superpowers that come from the Mind Gem, they were both new to the team as of 2015, and their incredible strength and unusual natures tend to freak other people out. They also both know more than they should for their ages, which is a big part of why they're freaky. Vision, as of the current date, is basically a year and a half old, but he has a great deal of memory from his much older programming--basically, facts with no experience. On the other hand, Wanda can read minds, which means she's constantly bombarded by the experiences of others. The movies have never specified her age, but my guess is that she's 19 or younger. So they've both got a lot to process. Plus, Wanda caused the vision that inspired Thor to bring Vision to life, the one that Vision is named after. (And they're both precious cinnamon rolls. IF YOU DISAGREE WITH ME, I WILL FIGHT YOU.)
On the other hand, Wanda and Vision are coming at the world from very different perspectives. Vision is innocent, with little experience in regards to suffering and hatred, where Wanda has suffered her whole life at the hands of others and carries a lot of anger and guilt. Vision represents logic, since his intelligence comes primarily from AI programming, whereas Wanda, with her telepathic powers and long history of pain and loss, represents emotion. Vision has a lot of typical "male" qualities (logic, strength, order, sweaters and button-up shirts), while Wanda presents as quite feminine (emotion, family, chaos, dresses and jewelry).
Also, in the original Marvel comics, they got married, so like, don't even try to tell me this isn't legit.
Like Wanda and Vision, Peeta and Katniss have a lot of differences that make them complementary. Katniss is as fierce as Peeta is kind, a fighter in every sense of the word. Katniss loves hunting, while Peeta loves art. In fact, they represent a subversion of the traditional masculine/feminine dichotomy. Katniss comes from the "rough" side of the tracks in her world, where the miners live, whereas Peeta is a townsperson, from a baker's family. Yet they have important similarities too: both have a incredible wealth of love for those closest to them and a clear sense of morality, and both have suffered greatly. Katniss experienced extreme neglect from her grieving mother when she was young, while Peeta's mother is physically and emotionally abusive--and, of course, they both experience the worst that their dystopia has to offer when they're selected to participate in the Hunger Games. More than anything, I love how Peeta brings out the softness in Katniss. He offers her safety and peace.
Also, like, he's been in love with her since they were in kindergarten! How cute is that? <3
Together, Rose and the Doctor are a formidable team, traveling through time and space to save as many lives as they can. Together, they make up for what the other has lost: Rose offers the Doctor companionship and helps ease his pain, while the Doctor offers her all the adventure and purpose she could ask for. Plus, they're adorable. :D
Their relationship is, I'd say, more tense and less sweet than my first three ships. They have the love/hate, constantly fighting dynamic, which is always quite fun and dramatic--though I don't think it's what I'd want for myself.
Obviously, you can see where the whole difference/complementary thing comes in. In common, they have a strong sense of loyalty and determination, and also the fact that they actually totally love each other. And, like, Matthias swears fealty to Nina. That's pretty legit.
Spoiler (highlight to read): Do NOT mention Matthias's death in the comments because I will COME FOR YOU. IT DIDN'T HAPPEN, OKAY? NOT A THING. I REFUSE TO ACCEPT IT.