You know, I used to have this same kind of attitude towards the ukulele. Not that it was a toy, necessarily, but that it wasn't really worth paying attention towards. It was a kind of ambivalent, "can anything good come from Nazareth" attitude.
But then a blogger I was reading said he was going to learn either the ukulele or the mandolin. In my mind, the mandolin was a much more legitimate instrument, but he chose the ukulele, linking to
"Tom Cruise Crazy" covered by sweetafton23 as justification towards what the instrument was capable of. I watched the clip and was pretty impressed, and so I kept looking at other videos. I soon had a pretty good list of why the ukulele was a valid instrument.
- It's much more portable than a guitar or other many other instruments. I commute a lot, and I have a lot of free time at one of my jobs, so I typically brought a guitar to play. It was pretty annoying toting it around, especially when I was in college and had to walk a quarter mile just to get to my car before driving the hour long commute. The ukulele, being both light and portable, was a much better solution.
- The nylon strings are easier on my fingers. I started off playing nylon string guitars, and never really played a lot of steel strings. So, even though my fingers have callouses, they're pretty dainty. When I did play a guitar with steel strings, it tore my fingers up like nobody's business. Also, it let me play fingerstyle, which I prefer to do any way.
- I really liked the size of the instrument from a playability perspective. The neck is much easier to get around. Also, I used to have problems with guitars making my right elbow ache from being so high. Before I got my ukulele, I was seriously considering purchasing a parlor style guitar because they have a smaller, more manageable body. The ukulele, being smaller even than a parlor, feels like a dream come true.
- I really like the tone. It had the same mellowness as a nylon string guitar, but it has a more delicate timbre that's also sweet. I was playing some instrumental stuff once, and my mom commented that it sounded like a music box. It's sound is really pretty in a moving yet quiet way.
So, I bought the ukulele as a kind of experiment. And over the nine months or so that I've had it, it's really become my go-to instrument.
After I got it, I took it into work that very night. A coworker was there, a guy who also plays classical guitar. We began talking about it, and he picked up the ukulele and strummed it a bit. When he gave it back to me, he complemented me on how it sounded. He even said he might get one. Also, I've got a friend who's a professional guitarist (I tech for his band). He's played it on a couple occasions, and he's told me that listening to me jam on my ukulele has totally changed his perspective about the instrument. The bottom line is, musicians tend to respect the ukulele. And not on a Ritz/Ohta/Shimabakuro/Hill level, but as an everyman instrument. They might not be the first to embrace it, but when they do, they like it a lot.
I hope those points help with your discussion with your friend.