...why does everyone make Leona a Support?
I do not understand this reasoning...
...really... other than her passive she has nothing to help partners that doesn't work just as well solo...
I do not understand this reasoning...
Leona is more tanky or AP I think...

Leona doesn't effectively work in any other lane. If they make one wrong move, her adc will instagib them. Because she protects, initiates and can get tanky enough for late game by running gp/10 and the gp/10 items synergize well with her. And she cannot be moved from the lane bushes. Just try. She also can zone out of the fear of god she puts in the other adc/support. Also, blitz landing a q on her is basically a free nice for her. She will just e-q-r and erase the carry.

Draven+Morgana
Draven+Taric
Draven+Leona
Draven+Sona
Draven+Lux
Draven+Zyra
Draven+Janna
Draven+Nunu

^Best bot lanes HUEHUE

Every ADC can synergize well with every support. It could be either offensive, defensive, or passive. Passive is the least favored playstyle while offense is the most favored playstyle.

Remember Graves + Soraka combo before Graves ASPD nerf? Holy hell that was an annoying lane to go up against.

Tank Mundo + Ashe

Skillshot snares/stuns of one make the other's easier to land.

Tristana + Sona = Agressive Lane
Graves + Taric = Early Game Armor
Sivir + Soraka = Sivir burns mana very easily
Corki + Janna = Shield works well on Corki

Don't just pick based on your lane partner, though. Make sure they fit your team comp well.

Hey men, have you tried Jarvan IV/Draven yet? It works pretty well, Jarvan deals nice damage at early game, he reduce enemy's armor and gives you armor and AS, a slow, a knock and his ultimate. You can 1v2 your enemies at bot, draven just throw his ult and is a double kill. Aaaaaaaaand his flag briefly ward, so you can check bushes and blablabla. It's funny, you should try it
(sorry for bad English and grammar errors, it's not my native language :P)

I might be flamed for playing Kayle as a support, but...

Kayle+Vayne is really good if you make Kayle tanky.
I had a game last night where we went up against a Leona and Cait. I zoned them out and XP starved them while Vayne farmed her heart out behind me. Leona would try to initiate off me and Vayne and I would just eat Cait every time. I kind of felt bad >_<;