Why are supports considered broken when we have champs like Teemo?

I have been a main from the very beginning. Now, i haven't been playing long however, most of the support champions i use are getting nerfed pretty bad. Almost every game i play most of my allies expected me to keep them alive and all my enemies enjoy hard targeting the support. This situation is a conundrum and a half considering we all get the main who wants to be a pro (and blames every death on the support) and the enemy who knows how to win a lane. Now my question has multiple parts, why are supports considered OP when they only have one or two combos that deal any damage at all? Why is healing so discouraged in game because the mana cost is so high or the actual heal does not even do a fraction of max health when we have champions like who can kill a champion with 2 mushrooms? Finally, why does everyone blame a support if the support is so nerfed that they can't heal or even defend themselves properly without someone to latch onto for the entire game? Overall, i just want to know why a squishy champion with almost no real damage output is in charge of saving an entire team. I'm sorry if this seems like a rant, i've just been seeing so many nerfs on champions who already struggle and buffs on champions who were already OP. Maybe league just isn't support friendly anymore or i should just take champs who aren't support to be the rescue champion like everyone else (looking at you teemo supports!).

EDIT: I mainly focused on teemo here but this is a callout to all the broken champions. tryndamere, shaco, teemo, draven, but mainly just champions who spawn in with an unfair advantage while supports have to struggle to work their way up the ranks. my point is, with champions so broken, why don't we look at them instead of already weak supports.