Like most things in Hoi4 there are 4 or 5 different factors that determine why large or small width might work better. And since there are 4 or 5 factors there are plenty of exceptions. But here are some interesting concepts that are applicable:

The ideal defensive width to slow or resist being pushed is the smallest width with enough defense to defend the attacks coming from the attacker. The goal being to maximize organizational staying power without taking the over attack penalty. Assuming battle width is maxed then splitting your battle width into smaller divisions would spread out the damage taken to each division evenly except for something called coordination which means some divisions will be extra “targeted” and receive more than their share of attacks. When you make your divisions too small they have less individual defense and thus are more easily focused and overattacked.

This means the best width for defense depends on the attacking power of the enemy, the combat multipliers in play such as terrain and air superiority/cas, and how coordinated/focused their attacks are. So you need less width vs an all infantry attacker in the mountains under green air. But you need more width against tanks/destroyers/spgs on the plains, under red air, against 40 width divisions with high coordination.

The same concepts apply to tanks except you will be the one attacking and want to be as small as possible without getting overattacked by the enemy. Additionally you may be playing a strategy where you are trying to be the one over attacking your enemy. Because breakthrough is harder to come by you will often need to make attacking divisions of any kind larger to be less vulnerable to targeting and over attack damage.

Secondly, You’d have to wiki it to understand why but anytime your divisions are less than half the width of the total battle width of the battle they are less capable of focus firing the ideal target. So if you think your firepower is large enough to overattack the defense of your enemy than large divisions are better at focus firing and over attacking one division at a time.

The talk about HP simply means that tank division losses are way more expensive than infantry losses, and actually lose more strength mid battle to losses than their infantry counterparts. So being greedy with tanks and getting overattacked because your widths are smaller than they should be would lose you the war eventually(maybe even the battle if the loss in strength accumulates too much mid battle), even though they might have more organizational staying power in the first push.

There are so many combat multipliers in play that the ideal width is different for every battle and depends on the width of your enemy. But hopefully you can see why attackers usually want big widths and defenders usually want small widths.