And I don't understand why. I've checked a bunch of different threads but no one ever offers any explanation on why it's a bad thing. My thought process on this is, as a champion who mostly relies on snowballing off roams, it would be a good thing. But I'm not in Bronze for no reason, so could someone clear this tidbit up for me?
xl Kirito lx2 votesThere's no reason to push the lane early. You probably aren't going to get a roam off bot lane, or zone at all. All it does is open yourself up to ganks.
Catastrop1 votesAh, so it's more of an early lane phase thing. I didn't take that into account, I was mostly thinking post Level 6-9.
Julanus2 votesNot a Katarina (or even an assassin player), but I'll do my best.
Anyway, I'd say she would only want to push the waves for roaming. Any other time, you'll wanna keep it to your side of the lane.
That said, I could also see the opposite. Theory-crafting here, but perhaps something like this.
Kat goes roaming, enemy laner pushes to her turret. Kat returns while the enemy is under/near her turret. Kat cuts off the enemy's escape, forcing the enemy to either burst Kat down or use their Summoner Spells/other abilities to retreat back to their turret/side of lane and avoid assassination.
Basically, like a Jungler, Kat ganks the enemy because they pushed the lane too far.
Like I said, I don't play Kat or any other Assassins, but being an Assassin without any real escapes, I could see that giving her an easy kill (or at least force the enemy to recall or stay at low health).
Spoofghoul1 voteshaha lol yea ganking ur own lane i do this with 
all the time lol
walk into river opponent starts pushing the wave back as he hears ult assuming im running towards my mates lane
He assumed wrong x'D
Zorasama1 votesMy guess is she has no escape if her ward isn't ready
Slamurai Jack1 votesKatarina is a pretty weak laner early on and can easily be denied from CS if you push too much early. Once you're post 6, you can then look to push and roam, although the enemy mid really shouldn't be letting you do this. Ideally, you'd like to push before roaming but your push is abysmally slow for a mid laner and most mid laners can outpush you if they choose to do so, so you'll often need to roam and hope it's worth missing CS and taking damage on your tower.