I assumed the little cats that sit farther forward was so they don't get back-endered while running the $hit, but I've mainly rowed round boats with centered oars.
As mainly a kayaker I like to push through stuff. I pull when I need to ferry away from rocks or holes, but any stroke that can be done forward, I do forward. Obviously a rower is stronger when pulling, so if a big ferry is needed, you should be pulling.
I see way too many rafters constantly rowing upstream, which is dumb on many levels. It slows the boat and makes it more likely to flip in wave trains, and slow boats annoy me if they manage to get in front and make me back row to stay off their tail. Scared kayakers tend to do this in class V as well and make the group clustered too close.
Schutzie will clarify;
The lessons I learned are for rowing, not paddling, not Kayaking. There are different lessons I learned for those rigs.
(I.E. when you are a kayaker you should always take the last beer, cause, you know, you're a kayaker and you wear a skirt.

)
If you're doing it right you rarely have to push while rowing; when you do push it's generally to correct an over zealous pull you just did.
The exception is when you hit the waves; pushing through them should pretty much keep you from getting into trouble and helps to keep you on your line. That is, unless you shouldn't have been on that wave in the first place. You know, cause it's bigger, faster, tougher and meaner than you are.
When I was rowing the pigs it was simple survival to accurately read the current. I wanted to be in it almost without exception, cause, you know, the current ended up doing all the work while I could just enjoy the ride. And a beer. It became a contest I'd have with myself, see how few strokes I could take in a day. My personal best was 18 strokes, from pump house to the bench, on a trip with a group nurses. And 12 of those strokes were to launch or land.
