Reels are tools, and for every job there's one tool that works better than another. You CAN split a rack of firewood with a maul, but a hydraulic splitter is gonna do the job more easily and efficiently. You CAN drive a 16 penny nail with a jeweler's hammer, but a framing hammer will do it much faster and with much less effort.
There's a time and place for both spinning and baitcasting reels. If I wanna skip a fluke under an overhanging tree, there's no way I could do it with a baitcaster, but if I'm planning on making a thousand short, accurate casts with a spinnerbait all day, there's no way I'd WANT to do that with a spinning reel. There are times when a baitcaster is a more efficient tool, and while yes, you CAN do it with a spinning reel, why would you want to? With a little practice and your reel's adjustments set properly, the baitcaster actually becomes LESS of a hassle than a spinning reel. Line twist is a non-issue, fewer steps to make a cast with no bail to fumble with, greater accuracy casting heavier baits (I'd argue anything over 1/4 oz), and more control at the moment the lure hits the water, which is where you get a lot of your strikes with reaction baits.
You can't really say which one is "better" in general...they're just different. But you can say pretty objectively which one is "better" for particular applications. It doesn't entirely boil down to personal preference. People just say that when they're less comfortable using a baitcaster due to lack of experience or having had trouble with one at some point and giving up on it. I'd be willing to bet that most people who have had bad experiences with baitcasters were either using a piece of junk, didn't have the adjustments set properly, or were trying to cast baits either too light or too heavy for the equipment.