Some people prefer Destroy because it is the only ending where Shepard can survive, but I don't know if it is accurate to say they're a majority.
Destroy is by far my favorite ending, and Shepard's survival never mattered to me. In fact I was fully expecting Shepard to die at the end of the game. Had Destroy been the only ending where Shepard dies, but saves galactic civilization, it still would have been my choice. I know from interacting with other people here in the years since ME3 released that I'm also far from alone in that opinion.
If you're looking to boil the popularity of Destroy down into a single reason, a more accurate one would be because it destroys the Reapers. People want the villains to lose regardless of whether or not the protagonist surviving is a must for them. Destroy is fairly clear cut in the villains losing. It ends with them dead. It is less clear with Control and Synthesis.
The "villain" to me is the Catalyst; the Reapers themselves are pretty much slaves... no matter whether you pick red, green or blue, the Catalyst is destroyed, so the options then become:
1: the Red (renegade) option : kill the Catalyst, its slaves, the Geth and EDI - save the organics. I say this is the Renegade option because it gets the job done, no matter the cost.
2: the Blue (paragon) option : kill the Catalyst, gain control over the slaves and save everyone else. I only say this is the Paragon option because you're getting the job done at the cost of your own life - although it's a slightly grey area since you've become the Reaper-god.
3: the Green (wtf) option : kill the Catalyst and "Reaperise" everything else! Every plant, every fungus, every bird, mammal, reptile and amphibian becomes partly synthetic... the Geth and EDI presumably get Reaper upgrades, like when Legion upgrades the Geth, mixed with some organic components somehow. Everybody lives but there's nobody cheering in the Extended Cut ending. Everything about it is a bit wtf...