I can think of several reasons.
1.) Maybe the beer isn't available in your region. For example, I'm in Canada. I recently had an opportunity to taste my first DFH 60 Minute IPA. It was delicious. I want more. But I'm in Canada and it's not available up here. So I found a "clone" recipe and made my own.
2.) Maybe the beer is no longer available anywhere. Maybe the brewery that made your favorite beer got bought out by AB-InBev and they've butchered the recipe to make it more appealing to the masses. Maybe your favorite brewery just plain went bankrupt and closed up shop.
3.) Maybe it's a seasonal beer that's only available certain times of the year.
4.) Maybe the brewery changed their recipe. One of my favorite beers was from a local brewery, but every few months, they change the hops they use to brew it. I loved it when they made it with Zythos hops, but their current batch uses Summit, which I'm not a fan of. So they shared the recipe with me, and I made it myself, using the Zythos hops I prefer.
5.) Cost. Note that this is near the bottom of my list, but for some penny-pinchers, it's a real factor for them. They can make an almost identical beer for less cost than buying it. Especially up here, north of the border, where a 6-pack of decent craft beer will run you $15.
6.) The challenge. It can be fun to see how closely we can duplicate our favorite beers, and you can learn a lot in the process of trying.
There's 6 good reasons right there.
All of these reasons resonate with me, especially number one. A friend of mine lived in Wisconsin and I was introduced to New Glarus brewery. I am a huge fan of Moon Man and their Black Top IPA. For me it involves traveling three states to get their craft because they don't distribute beyond WI, and have stated on their website that they have no desire to distribute past WI. If I want New Glarus, I must travel or clone my own. Within hours I was trying to find a recipe.
Since then, my desire to clone it has faded somewhat, partly because of the difficulty in finding anything about the actual hop blend they're using and my own misgivings that it'll even be possible for me to source the ingredients or get it right. Pliny the Elder is another one that sounds very tasty, and I'd be happy to brew a clone - knowing full well it's not the beer that is sold commercially for something close.
This discussion about clones brings to mind an article I recently read about folks who try to recreate movie props, in this particular example, Han's DL-44 blaster. Similar to brewing, it's very difficult if not impossible to precisely clone the prop. Instead of malt, mashing, yeast, and process differences they are faced with the challenge of inadequate source material and a virtually infinite number of parts to draw from to try to get it just so. But they really don't want the prop to be a perfect replica - stage props are imperfect and often incomplete because it only has to look correct in context of the shot. They don't make perfectly detailed stage props because they'll be thrown around, dropped, broken, and generally take abuse. These props will even vary between movies in a series, or for different shots. The most accurate props are used for publicity shots and even then they will vary between individual units. What a replica builder is really trying to recreate is what they
think the prop looked like. What their imagination built for them as they watched the movie. What their imagination built is probably better than the actual prop recorded on film.
While the replica creators goals may change as we move into 1080 and 4k movies, for me cloning resembles making prop replicas (especially of older films). I'm not so much interested in cloning
exactly what the brewery released as I am in recreating what I
remember drinking. I suspect my memory of that first Moon Man is better than what was actually in that bottle.