Here's the reasons I can think of:
Using protect can let you see how your opponent is going to move and allow you to uncover some of the moveset, so then you can make good switch-ins and fight back.
If you have a blaziken, sharpedo, scolipede, yanmega, or ninjask (for baton passing), use protect to get a boost!
In weather and/ or your opponent is burned/ poisoned, use protect and 0 damage to you, and they lose a bit of hp.
If you have leftovers, or aqua ring/ ingrain active, you can heal a bit.
5.Mega Speed Increase
If you didn't know, when you megavolve, you don't get get the mega's speed stat on the turn you mega evolve. Use protect to get get this boost (use on mega beedrill).
6.Aegislash ( King's Shield)
Use this to change form to defense form so if you use this every other turn (and you are slower than your opponent), you basically have 150 offense and defense. Also you lower attack of contacters (Blaziken is in Ubers like Aegi).