I feel like that's what most fail to comprehend.
They do want to win, but they don't want a win where they are "carried", they want a win where they stomp and are the MVP, so having supports that may end up taking kills is "bad for them".
The other way around is a bit different because it's Yolo que, so people wanting more agency as a support is understandable. I can be a godly Soraka but if my ADC is dumber that Yorik's zombies, all I can do is be a bit annoying and hoping the other lanes can carry and if that doesn't happen, it's gg, while a damage support can buy more time for his team by slowing the enemy which can swing a bad game a bit more often than what a good Soraka can.
In the end a win is a win and many don't want to win unless they carry hence the "You didn't help me when I went 1v5 for the YouTube montage so I'll int" mentality a lot of people seem to have, especially in lower elos.