I started making wine and mead about 6 months after I started brewing beer, because I was curious how other stuff besides malted barley would ferment. Also, SWMBO is not much of a beer drinker, so making wine that she likes gets her more excited about my brewing hobby. In fact, now I've ruined most commercial grape wines for her, because she prefers the ones I make.
I brew beer for me, and wine for us.
On a related note, the kinds of country wines you can make with all kinds of fruit are unlike anything you can buy, which is exciting to me, and feels like a more like a blank slate for recipe design than beer. I enjoy prowling the juice aisle of the grocery store for tasty fermentables. However, now that I make wines, i find that I can appreciate good grape wines more than I used to.
I mainly drink my homebrewed beer, but I do enjoy having wine aging and developing. Also, wine brew days are usually easier because there is no wort to boil. Its mainly just "dump and stir" as I like to call it. And wait. And wait. On the flip side, wine just sits there most of the time, so its easy to just forget about it while you have beer going, and then occasionally fiddle with it as needed.
I started my winemaking adventures out with Skeeter Pee aka Lemon wine because it was cheap to make in case i screwed it up, and am very glad I did. It has step-by-step instructions that really introduced me to many of the subtle differences in the wine-making process from beer, and can be bottled in under two months and is very drinkable on bottling day. Oh, and its delicious.
As a beer brewer, its tough to bottle several gallons of your first wine and have it sit there for a few months aging, wondering if it'll even be drinkable. Hard to refine your process for a second batch of wine if you still dont know how the first turned out. Thus those first few quick batches of SP helped me learn the ropes before I tried more involved, expensive wines. Also, a batch of wine is a really long-term commitment, and I didn't want to use my limited storage space for 6+ months with bottles of rocket fuel.
I should add as a disclaimer that I have never bought a wine kit or made wine from wine grapes. Mine have been Juice wines and pyments, some from whole fruits, and the Skeeter Pee I mentioned, so I never went into this winemaking thing with any intention of duplicating any commercial style, and thus my experience and goals may be different than most.
I think winemaking helped me be a better beer brewer as well, and I would recommend you try it if you have any interest in drinking wine at all.