"But now the U.S. government has asked us for something we simply do not have, and something we consider too dangerous to create. They have asked us to build a backdoor to the iPhone. ... Opposing this order is not something we take lightly. We feel we must speak up in the face of what we see as an overreach by the U.S. government. ... And ultimately, we fear that this demand would undermine the very freedoms and liberty our government is meant to protect."
Upd.: OK, as _winnie and others pointed out, it does raise questions about Apple intent and competency of people who wrote the letter (and/or perhaps mixed with the fact that Apple can't disclose certain things). One - it exposes the fact that Apple already had a way to break into encrypted data. Two - although it may initially sound like government demands mass backdoor, it actually doesn't (yet) so there's a lot of speculation.
Regardless of what's Apple intent and interest here, I hope public opinion will interpret it as fight for freedom of encryption and will lead to more proper implementation of security in Apple products and elsewhere in IT.
Upd.: Google joins in: http://www.theverge.com/2016/2/17/11040266/google-ceo-sundar-pichai-sides-with-apple-encryption
Upd.: According to USA Today (http://www.usatoday.com/story/tech/2016/02/16/heres-why-fbi-forcing-apple-break-into-iphone-big-deal/80481766/) this isn't about encryption, but about a feature that deletes (possibly unencrypted) user data after several invalid attempts to enter pass code.