Why is organization important in building an argument?
It helps make the argument more compelling.
Building an argument is much like any other type of communication - it often best understood when it is organized.
Take this answer as an example. I've opened the answer with a generalization - that organized communication of any sort, not just argument, is best when organized. And now I'll go on to demonstrate why this is.
Your brain is lazy. What we think we see is based largely on expectation and inference. There are a series of paragraphs on the internet demonstrating how it can read words based solely on the first and last letters being correct and all the other intervening letters being present but not necessarily in the right order, like this one:
I cnduo't bvleiee taht I culod aulaclty uesdtannrd waht I was rdnaieg. Unisg the icndeblire pweor of the hmuan mnid, aocdcrnig to rseecrah at Cmabrigde Uinervtisy, it dseno't mttaer in waht oderr the lterets in a wrod are, the olny irpoamtnt tihng is taht the frsit and lsat ltteer be in the rhgit pclae. The rset can be a taotl mses and you can sitll raed it whoutit a pboerlm. Tihs is bucseae the huamn mnid deos not raed ervey ltteer by istlef, but the wrod as a wlohe. Aaznmig, huh? Yaeh and I awlyas tghhuot slelinpg was ipmorantt! See if yuor fdreins can raed tihs too. https://www.ecenglish.com/learnenglish/lessons/can-you-read
The same is true for any sort of communication - the brain expects to hear what it thinks is true. It actually takes a bit of work to get it to change its thinking. Having an organized argument aids someone to follow a new line of thought and for the argument to be effective.
Organization also helps communication be concise. Have you ever listened to a long-drawn out speech where the speaker repeats him/herself repeatedly? Lack of organization leads to communication that bores the listener and makes an argument less compelling.
Lastly, I'll compare a lack of organization to a 4-year-old telling a story - the story is usually all over the place with tangents and side notes, often it runs on and on and on with no end in sight, and usually in the end makes no sense at all. That is what an unorganized argument can sound like.