Erh? Are you complaining about some minor adjustment, so that lines are not meeting the curves smoothly? I did not even understand what TANGENT means, cause I know much nothing about CAD.
I've overlaid your part on the correct part (as best I can when working with the mesh files that come out of OpenSCAD). Your part is drawn in red: https://i.imgur.com/12y5q1t.png
Yes. Lines should touch circles in a smooth way. There could be many arguments why it's kinda important. Like fit to other parts in a final assembly or production complexity. But even for DIY purposes this minor adjustments would suck a lot of blood in prototype phase, it's a way more simpler to constraint it to be smooth (tangent) and forget about all tweaks needed after dimension changes.
You absolutely don't need to get into the maths to get value from this idea. The maths terrifies me. Just know this core concept: a tangent line meets a circle only once and is at right angles to the radius when it does.
Here's why this is valuable in CAD environments that properly support it: once you know how a tangent line works, and see how a constraint-based modeller represents them, it is possible to understand how to model a whole set of smoothly rounded features that the CAD package can automatically adjust to changes made to core measurements, retaining this perfect "join". Rounded slots, curved rounded slots, fillets, all sorts of interesting motion components, etc.
