I like your analogies approach, that's also my go to. The one I use a lot (there are probably better ones for this). HTML is like the human body's bones, CSS is like your physical apprecance and javascript is like the muscles and joints so things can move and interact.

But in addition to the analogies, I also show in real time what an example of that looks like on a website, for example javascript I show a something interactive with javascript on the site and even some obvious code like "on click". I also show examples that weren't created by me and sometimes I'll post an intro tutorial video or have them read an article on the topic.

In your case, with SEO, in addition to that analogy, show them the SEO process in real time, and if they still don't know why you're doing it, maybe send them a video showing similar processes or looking at another freelancer/site/whatever that does the similar process.

If your client doesn't budge on requirement standards then he's probably tough to crack. This depends on your ethics, but I'd probably make up a somewhat "believable lie". I'd tell them the truth, saying SVGs retain their quality at all sizes which is great for all devices (and show him compared to like a png). Then I'd make a "believable lie", something like "if you don't use an SVG, you're gonna get lower customer reviews". Is it true? IDK, but it's a pretty "believable lie". And that's in addition to the fact of the standard.