Matti, as someone who wasn't even born until 1993, I can understand... not understanding the appeal of something that was before my time. Heck, there are things from the 1990s and later that I just don't get!
That being said, I think part of the appeal of muscle bikes and muscle cars, from a retrospective point of view, is that they stand out among the crowd now as much as they did when they first came into being. Before the mid-60s, cars and bikes were... cool, but kind of mellow, at least when talking about factory-built cars and bikes. Cars and bikes alike were mostly pastel-colored, kind of slow and leisurely as far as performance goes, still pretty flashy in some respects, but they didn't do a lot of "tricks."
Then around 1963/1964, you had the Pontiac GTO and bikes like the Huffy Penguin and the Schwinn Sting-Ray, and BAM! They were unlike anything that came before them, and in many cases, unlike anything that came after. They came in a wide variety of loud, in-your-face colors and graphics, with equally bold names to match. Muscle bikes and muscle cars were about being bold, and showing off doing tricks of all sorts. Muscle cars went fast, had enough power to pop wheelies, came with a stick-shift and a tachometer, could do burnouts for distance and donuts for days, and they were every bit as crazy as the 1960s were. Likewise, muscle bikes came with the option of additional gears for more speed, they had stick-shifts, you could pop wheelies on them, and in the case of the Swing Bike, you could even turn on a dime or "drift" down the cul-de-sac.
And even today, if you see a vintage muscle car or muscle bike, it looks nothing like what they make today. Sure, Dodge has been bringing muscle back, and even Ford and Chevy did for a while, but they can't replace the raw, gritty, and just plain crazy vibe that those 1960s and 1970s originals had. Likewise, there have been some updated reproductions of vintage muscle bikes, but they aren't quite the same as the old ones. Plus, given how most of the bike market is focused on high-end high-performance bikes, with electric assistance, heavy-duty suspension, new lightweight materials, all typically wrapped in the same tried-and-true diamond design, those old muscle bikes from the 60s and 70s just pop! Sure, they may not make great daily riders, and they may not go as fast as bikes can today, but they offer a glimpse into a decade that, in my opinion, is the crazy, loud-mouthed, party-going, somewhat scary but still incredibly fun uncle of the 20th century family.
So, yeah. That's kind of my take on muscle bikes/cars and why I find them appealing even though they were before my time. They're different, they're weird, they're crazy, they're unlike anything made today, and they're awesome because of that.
I didn't expect to type this much, but I like discussing these kinds of topics.