I know the usual answers - stability, KISS, etc, but as a newbie(ish) to Linux in general and Slackware in particular, I almost think this question (which comes up repeatedly) is almost missing the entire point of Slackware.
I've decided that the answer (for me) is that Slackware is the craft microbrew of Linux distros. Painstakingly created, tended, and bottled by one man (with some diligent helpers). No, it doesn't have the flashy ad campaigns of the majors, or the ease of (X), but you can tell someone has taken their time with this distro, and crafted it with care and love. Pat V. has a vision, and this is it. That appeals to me in intangible ways that a simple list of the technical 'advantages' of Ubuntu/Arch/etc does not. It's not to everyone's taste, but I don't think it was ever meant to be.
I think he's done an incredible job making a stable, secure, fast operating system that makes sense. I've tried really hard to use Debian/Ubuntu/others but always come back to Slackware after scratching my head for hours wondering "which file do I edit to this?" when the answer is actually "which distro-specific script do I run to do this?"
I'm extremely biased because I've only ever used Slackware seriously (for servers and desktop) but trying my best to put that aside, I think it's a masterpiece.
There's a cred to it too, which is no reason to use something, but it's the icing on the cake. In some of my support jobs, I had to interact with other techs, and once in a while you get a BSD snob who says "Oh pff, you're into linux? What distro do you use?" and after hearing "Slackware" the tune usually changes: "Oh! You probably know what you're doing then." I think it's true, though: if you can manage a Slack server, you can probably manage any server. The reverse is probably not so true.
I've decided that the answer (for me) is that Slackware is the craft microbrew of Linux distros. Painstakingly created, tended, and bottled by one man (with some diligent helpers). No, it doesn't have the flashy ad campaigns of the majors, or the ease of (X), but you can tell someone has taken their time with this distro, and crafted it with care and love. Pat V. has a vision, and this is it. That appeals to me in intangible ways that a simple list of the technical 'advantages' of Ubuntu/Arch/etc does not. It's not to everyone's taste, but I don't think it was ever meant to be.