Why would Switzerland, with its export-driven economy, worry about weakening against the dollar? I was reading about the SNB's decision to abandon the peg in 2015, and among the various articles I read, one from CNBC quoted the SNB president saying the following


  "The euro has depreciated considerably against the US dollar and this, in turn, has caused the Swiss franc to weaken against the U.S. dollar. In these circumstances, the SNB concluded that enforcing and maintaining the minimum exchange rate for the Swiss franc against the euro is no longer justified," the statement said. 


My takeaway from this statement is that part of their justification for removing the peg came from the effect it was having on the franc's value against the dollar.

I know they wanted this peg in the first place to lower the franc's value against the euro as Switzerland's economy was largely reliant on exports to euro zone countries, so having a weaker currency than the euro would help exporters.

But I don't understand why the franc's performance with the dollar would be a concern? Wouldn't that just help Swiss exporters sell to US importers as well as Europeans? Or does falling below the dollar have other consequences?
Its not totally clear, but it seems that what they are saying is that, as long as the euro was a strong currency, they did not want to have the frank much stronger than the euro. Later, on, when the euro lost value, they no longer wanted to insure that the franc wasn't much stronger than the euro.

In other words they don't want a very strong currency, but they are ok with having a stronger currency than their neighbors. 

The question includes just one of the concerns for central bankers. It says that the Swiss export to their neighbors, so they don't want their products to be uncompetitive with those of other Europeans. That would mean less purchases, lower GDP etc. This was the logic used when they imposed the cap on the franc price relative to euros.

However, the central bank has another main concern, which is that it wants to make sure the currency remains a good asset for investors. It has to make sure the currency doesn't lose value, otherwise, it hurts all those investors that trusted in it. So, for the world wide capital markets to demand the Swiss franc, the central banker needs to maintain a reasonably high value for it. This is the core concern when they are allowing the franc to increase in value relative to a (falling) euro.