Protect is by far the most used moved in any doubles format and there are a number of reasons for this. To keep things organized and digestible I’m going to spilt these reasons into separate sections.
1: The biggest reason to use protect is its ability to position yourself. For example if one of you Pokemon is threatened you could protect the threatened Pokemon and switch the other Pokemon to something with fake out so you can fake out the opposing Pokemon that is threatening your protecting Pokemon.
2: Another use case for protect is prediction. For example if you have a Pokemon thats set up and you think your opponent is going to double target your set up Pokemon you can protect that set up Pokemon and use your other Pokemon to get some free damage or get a free switch.
3: This final use case is more Pokemon reliant but it’s using a protect move for its secondary effect. This is most common with Pokemon like Aegislash where you need to protect in order to get your defense stat back but there are other Pokemon who use protect in a similar way like Gouging Fire fire using Burning Bulwark to burn things or spiky shield to chip things. Using protect moves with the goal of using their secondary effects is not always worth doing as it can be a bit of a momentum sunk but if you can burn a powerful physical attacker with Burning bulwark or break something’s sash with Spiky shield it certainly can be worth using the protect move with the goal of using its secondary effect.