I both love and hate technical explanations. The love part comes in where understanding a concept is involved so technical explanations can help cement the idea when "doing the deed." On the other hand, techno-babble and the pseudo-intellectual pursuit of ideas can make one out to be a closet philosopher and not much else.
In any case, I'll throw a few things to consider in the tai-sabaki pot. These are coming from my vantage point, stylistically speaking, so qualify this as some nonsense from another goof on the internet that you can think about or disregard at your leisure.
But, yes, generally stepping outside, and sometimes inside can offer you a better position from where to hit. But it can be a little bit more involved, so the question is why is it better to move a certain way than another and what advantage will this offer you? In other words, what strategy can I look for to invest in my movements so that I can be in the superior position?
I'll relay some thoughts that I had let a few people take a look at, but this might give you an idea of where I am coming from. Be forewarned, it's a bit long and you might just want to skip it.
In this consideration, tai-sabaki is, foremost and fundamentally, a selfish construct to place you in a better position to attack from. Ideally, your opponent is concerned with momentum recovery while you place yourself in a superior position, and this is why parries are more generally used in our style than hard blocks. This is so you don’t stop the opponent for his quicker recovery, but allow him to continue onward in a direction that compromises him and not you. Also, one of the key points is that you don’t duke it out with the opponent, despite being able to handle it ala Kyokushin. You are always trying to reduce taking damage. This is fundamental so that you can better extract yourself from a situation in case things go badly-to-worse. Taking damage, despite initially being able to handle it, can weaken defenses and allow later entry into your guard. So defense first, offense second. Therefore body positioning is more important that being able to strike well. Poorer strikes from superior positions offer better advantage than really hard strikes from compromised positions.
Basically, if you look at kazushi in Judo, or some unbalancing that is done in Aikido, the relevant principal holds true. You are unbalancing along lines generally 45 and 90 degrees to the plane of your opponent’s attack.
If you consider what I have stated above, you must have a fundamental knowledge of how one attacks…that in order for the punch or kick to be effective you have to translate your body weight into the limb…this means lunging or torquing. Doesn’t matter how it’s accomplished, but your mass must swing through like a batter fluidly swinging a bat to hit a ball. That also means that in order to strike you, the opponent is shifting his weight onto one side or the other of his body to deliver this strike. Where the weight is distributed will allow you to focus your attention on where to destabilize the opponent.
Once you identify the person’s strike, he has to recover that same body momentum before striking again, recover hip alignment, recover his balance, etc. Now if you can parry the strike or slip it, what you have done is allowed him to continue on an altered path from his intended one, but have not stopped his momentum while you have time to position yourself for a better counter before he can recover to continue his assault. So TIMING is critical!
For unbalancing, an easy way to see this is to have a person throw a straight right or a reverse punch. Just go to the side of the individual, as if slipping the punch so you are just outside the arm that is punching, and pull on the punching shoulder along a 45 degree line from the direction of the punch, you will throw your partner off balance because the inherent weakness in the stance. You can also push along that same line, which honestly, our style would probably more often do, and since the weakness in the stance is there as well, the opponent will stumble a bit to recover and you have an opening for an attack from a superior position.
Again, when striking or kicking, your stance is functioning as a platform to throw an efficient technique. It is meant to bolster the body--and in the case of a straight technique, is fore and aft of the performer, but not to the side. So inherent weaknesses are always in the offing when someone strikes, but one has to capitalize on them. For circular strikes, similar things can be done, but is a little less easy to describe, so I’ll skip that.
If you accept the definition I am using of a stance as either a snap shot of a movement placing you into a particular position of your choosing or as a platform from which to strike from, then the reverse is true: that if the attacker’s weapons are aimed in a particular direction, then the platform’s orientation from which to launch those weapons is not as valid for support of those strikes to other directions. This is a cursory explanation, but might offer you an idea of where to go and why when moving around an attacker's strike.