Here's the perspective of someone who loves playing devil's advocate:
1. I will play devil's advocate if someone mischaracterizes the opposition's arguments. To me, it is intellectually dishonest and poor form to argue against a shitty caricature or strawman of whatever it is you disagree with. It is not fair to the other side, who are not there to defend themselves from terribly constructed arguments lobbied at them.
2. Sometimes, I'll mentally construct arguments in the same way mathematicians formulate proofs. I'll select a bunch of axioms/postulates/assumptions/etcs and go, "Well, I have collected a bunch of axioms/postulates/assumptions/etcs. Let's see what comes out of it." And I'll construct an argument that's hopefully logically consistent. But is my argument truly logically consistent or do I merely believe and wish it were so? Eventually, I'll need input from other people to proofread the argument, so to speak. So what does playing devil's advocate have to do with this? Well, the assumptions I've chosen are not necessarily ones that I personally believe in. I treat the whole thing as a form of mental exercise to keep the mind sharp. And if those assumptions are ones that I disagree in and, in fact, believe in the opposite of, that runs into devil's advocate territory.
3. Playing devil's advocate of the opposition allows you to find weaknesses and holes in their argument, and, in general, "feel the rhythm" of the argument. What are its strengths? What are its weaknesses? If done right, playing devil's advocate also means finding counterarguments to the devil's advocate. And what do you know, the counterarguments of a devil's advocate are the counterarguments of your couterarguments ie your arguments.
4. I use playing devil's advocate as a measurement of how much I grasp the opposition's arguments. The shittier my devil's advocate is, the shittier my grasp of the opposition's argument is, which casts doubt on how strong my actual arguments are. How can I be so sure of my arguments if my grasp of the opposition's argument is weak and flimsy? Because if my grasp of the opposition's argument is weak and flimsy, then what's more likely is that I haven't truly thought deeply of an issue rather than me being far smarter and better as a person than them. "They only believe in X because they're assholes" is never a good sign.