There are many reasons to play the accordion.
Firstly, it's different. You see a lot of violinists, pianists, cellists, etc., performing all the time. But when is the last time you saw a serious, professional accordionist playing? Although the stereotype accordionist plays only simple folk polkas, in reality you can do a lot more - provided you have a full-sized instrument, both jazz and classical music are not only possible, but are surprisingly well suited to the instrument. A well-maintained, quality accordion has a pleasing sound and large dynamic range comparable to a piano or woodwind.
You can play without having to be accompanied all the time (something that string and woodwind players cannot do). You can also sing along while playing.
By playing the accordion, you will also develop a large degree of manual dexterity and develop strength. Playing complicated music requires a lot of finger work in both right and left hands, and operating the bellows is an excellent exercise for the left arm.
Moreover, there is always demand for accordionists. If you play well, you can be hired as a performer at a restaurant or other venue for good money.