"Teppo units on the flanks"

Well historically they moved in front of the main battle-lines, quite a bit ahead with small contingents of yari ashigaru to support against cavalry shocks. Basically skirmishing between the ahead troops could go on for quite some time and often took up the majority of battles. The progress of their fight for ground would affect the possible main clash between the great bodies of troops, however, often an army would withdraw even before that when the daimyo realized that they had been pushed into a losing position and a battle was most likely just going to be a waste of men.

However, if and when the main lines clash, I'm sure it made sense to send your skirmishers out to the flanks, since they would by then be withdrawn to the rear, free of locked battle. Then from the flanks they could either soften up the enemy lines, move further around to maybe charge home, or most likely, end up skirmishing enemy forces trying to do the same to you.

"caving the whole center inward, the ultimate goal of battle."

Breaking the enemies lines, either by folding up the flanks or punching through the center and seperate it would typically become the main objective once battle was joined because that was the foremost key to victory. By simply lining up against eachother and hoping your enemies would break first, like old-school greeks you would only waste men. So you tried to focus on various strategies to break their morale faster and more certain. Seeing your flanks being rolled up on you is one of the things that does this.

"Cavalry will be trying to circle wide and fight each other"

I think he means that often, if the enemy also has cavalry(they often do), he would use it to stop any flanking attempts, which may result in cavalry fighting it out before it's determined which side gets to flank or charge home.

I can't say I have played much TW multiplayer myself, only a little on LAN, however, having vanilla TW MP experience under your belt reveals little about insight into realistic battle-tactics. Often what would make sense in reality is comepletely useless in games because they model things unrealistically. Many elements that were all-important in real combat becomes a waste of time and things may be very simplified. Our mod will hopefully be designed so that you will be encouraged to use historical strategies(at least in MP) because the units will not be balanced after some simplified rock/paper/sissors-policy for a shallow RTS-experience, rather how armies were actually organized.