Anyone who's been on the forums for some time has been through the Riven hate several times, and as such have had their opinions on her galvanized. It's one of the oldest circlejerks, and even now still sticks around (no pun intended).
Anyways, Riven's kit has a simple design. She has her mobility tied to her damage and survivability, so she must use her abilities wisely to get the most out of her kit. Whether against melee or ranged, she doesn't have a flowchart to follow in order to win and can be exploited as her damage takes time to come out. There are three things that break her, and each one revolves around a simple fact: if Riven is able to bypass any part of her damage combo, her counterplay significantly drops. This is due to her massive shield and multiple CCs. Riven is only balancable around a long-term damage paradigm, which is why she snowballs so hard when she gets ahead. These are the three main culprits that cause this:
First is that her passive is the only part of her kit that has counterplay. Q, W, and R to an extent are fast and unavoidable. The only part of Riven's damage that has counterplay is the speed of her basic attacks being slow (as mentioned above). This means that if Riven wants to kill opponents better, the passive is the first thing to go. But it's the only thing holding her counterplay together, so the moment Riven can cut out a basic attack from her combo, her counterplay significantly drops.
Second is the animation cancel. Riven will pretty much never build Attack Speed, which means that use of her passive takes time. If she burns all her Qs straight away she has to spend several seconds attacking as a squishy melee, and if she uses her Q between basic attacks. Either way, there is a lot of time to react to her and fight back. The animation cancel she has lets her put out damage much faster, which leaves much less of a window to fight or flight.
Last is her R. R gives a massive damage boost as well as a ranged AoE execute. The amount of damage that it gives is ridiculous, as is befitting an ult. But, the amount of power it gives makes Riven incredibly binary. If Riven is capable of killing people without R, then R allows her to kill people with too much counterplay removed. If Riven needs R to kill, then she is too weak without it and is too easily exploited. Riven needs to be able to fight people all of the time because she is squishy and completely melee. Her R does not fit with her kit at all.
tl;dr, the problems Riven's balance faces are as such:
Riven only has counterplay when she must use her passive stacks to kill
Riven must be able to fight her opponent all of the time, or she will be binary
These are the things that break the first one:
Getting ahead enough to kill with less basic attacks
Animation cancelling significantly reducing basic attack time
R's raw power
The second is broken by getting too far behind, as she cannot farm safely.
This leads me to a simple conclusion: Riven needs one of her abilities removed and replaced with an ability that has counterplay, and it needs to be a significant part of her damage output. This will prevent her from facerolling over people when ahead, since this will let opponents always be able to fight back at her. As for which ability, W is the most boring of her abilities and is a prime candidate, but her R is very problematic to balance and might be a better choice. Either way, numbers on her other abilities will likely need changing as well, but a new ability will put her in a much better place for balancing.