For myself, there are three main reasons why I prefer being a DM over a player:
1) Attention Span:
I honestly have trouble sitting and focusing while playing! I'm usually drawing in my notebook, playing with dice and miniatures, etc. In my last long-term campaign as a player, I purposefully played a wizard who never cast damaging spells because I knew I would want to take time to think about how I could use illusions and utility magic to help in combat!
As a DM, my mind is always occupied. I'm always thinking a few steps ahead, engaging with players, checking and rewriting my notes... I hardly have time to get up to pee or drink a beer (maybe there's a connection there?), and after a good session I have that wonderful tired feeling of having my mind fully occupied for a few hours.
2) Endless Creativity
I love, love, love the creativity of running a game... especially between sessions! Others have mentioned making maps, and the design aspect is really fun for me.
When I start a new campaign, my brain is just on fire with all the possibilities. It's a fun process to coral all those wild thoughts into the format of a D&D setting.
During the campaign, I really enjoy thinking through what's happened, what's ahead, and how I can adjust the game to be an even better experience for the players. It's endless creativity, and I love that.
3) Showing my Friends a Good Time
I play almost exclusively with my friends, and it's honestly one of the greatest feelings when they have a good time playing in a game I'm running. It's the same feeling I get when I invite friends over for a homemade meal (if I roll well in the kitchen), or take a friend on a special hike or bike ride. D&D gives me that unique ability to craft a really fun experience for my friends, and I love it.