Ana's Biotic Rifle heals for 75hp per shot. Her Rate of Fire is 1.25 rounds per second And she has 10 rounds per clip.
That's 750hp in 12.5 seconds.
To put that in perspective:
In 12.5 seconds
Zenyatta heals 375hp
Mercy heals 750hp
Lucio heals 156.25 minus Amp it Up - 264.25 with Amp it Up
With just this Ana wouldn't be broken. She'd be just under Mercy for single target healers when calculating missed shots and damage.
When you add Biotic Grenade though everything changes.
Biotic Grenade heals for 100hp and +100% healing from all sources for 5 seconds.
To put that in perspective:
In just 5 seconds with Biotic Grenade
Zenyatta heals 300hp
Mercy heals 600hp
Lucio heals 125 minus Amp it Up - 360 with Amp it Up
Ana heals 600hp + 100hp for anyone she hit with the grenade.
This means with Biotic Grenade it takes Ana 3 rounds or 3.75 seconds to almost fully heal Roadhog and she can do that every 10 seconds.
Remember none of this math takes into account the fact that there has never been a 1 healer meta so other healers will be around nor does any of it take into account self heals such as Roadhog, Soldier, Mei, or Reaper.
TLDR: People on this sub cry "Ana is broken" because the math clearly proves that she is.