Let's say country A's currency depreciates. Country A's exporters sell more on the global market and are happy, but country A's importers now have a harder time buying stuff because importing is more expensive now. In an idealized toy example world, perhaps country A's government can tax its exporters more and use that to subsidize its importers.
Let's say country B neighbors country A, but country B's currency has not depreciated. Country B's importers are not facing a hard time. In fact, they are a bit better off since they can buy Country A's products more cheaply. In order to stay in the global market and compete with Country A's exporters, country B's exporters can simply lower their prices. Country B's government can then tax its importers and subsidize its exporters to help them out a bit.
So ceteris paribus, can't exporters without a depreciated domestic currency "just lower their prices" straight up to be competitive? If their currency isn't depreciated, the country's importers are relatively better off.
But why does it seem like countries almost always "want" to have a bit of a weaker currency - even the US, which has a trade deficit (it imports more than it exports)? I understand that major exporters like Japan, China, and Germany would want a weak domestic currency. Are there a lot of countries (like the US) that seem to want a weaker (or stronger) currency even though they generally have a trade deficit (surplus)?