Because you are a special snowflake, who really, really believes in what you're doing; your feelings about something make you so special that the law just ceases to apply to special little you.
And it's not like conservatives are going too far out on a limb in believing this. In some measure we've come to accept that belief should excuse you from following the law, even as it impacts others. With, for instance, Hobby Lobby, we see a shift toward the idea that your beliefs, even if factually wrong, simply exempt you from the law -- even when, in practice, that has an impact on other people. We've moved away from the sensible idea that a person shouldn't be held to laws that conflict with his beliefs where exemption won't have an impact on others, to a world where religion is a valid excuse to get out of such obviously necessary things as driver's licensing rules. So we've gone from "your career won't be ruined for using a prohibited substance in your religious ceremony" to "you don't have to provide health care coverage for medicine you don't like". Religion and religious belief has become the trump card: having a belief about something, in a sense, did make you a special snowflake, and you could get away with all sorts of things, regardless of the impact on other people, by virtue of how special you were.
All animals are equal, but animals who profess a strongly held belief are more equal.
Or so conservatives, and their overly broad interpretations of religious freedom, seem to have convinced themselves. And then along comes the Indiana skirmish, and all of a sudden this isn't a given any more. Along the lines of "your right to swing your fist ends where the other fellow's nose begins," people, it seems, are not willing to make the same allowance for belief when it impacts people beyond the believer as they are when it concerns just the believer. In other words, people still haven't lost sight of the only sensible view of religious liberty there is: we should all be free to live according to our consciences, up until the moment that those consciences drive us to impose our beliefs on another person. In a world full of competing, often contradictory ideas, this is the only view of religious liberty that is feasible, or could possibly be evenly applied.
And it's a far cry from the special snowflake syndrome conservatives seem to be suffering from...because, at the end of the day, none of us are or should be special snowflakes in the eyes of the law, and none of us should have a trump card to use at the expense of our neighbors.
(Image info: "Unique, snow flake" by Pen Waggener - Flickr: Unique. Licensed under CC BY 2.0 via Wikimedia Commons.)