This is because you are applying the dissolve in the last frame of the clip.
The clip needs some tail to make the dissolve.
If you want to apply a 1 second dissolve, this needs to go (at least) one second before the end on the clip. The same happens for the clip you are dissolving to.
Shane's Stock Answer #1: Trying to add a Transition and get the error "Insufficient Content"
A full 1 second cross fade reaches 15 frames into each clip. So, if you want to change a cut to a cross fade, there has to be at least 15 additional frames of each clip. Say you're trying to cross fade from one clip into the very first frame of a second clip. FCP cannot 'create' 15 more frames of the second clip to do a cross fade. If they're not there, you're out of luck.
What you are running into is that you are marking an out point at the far edges of a clip then adding a cross dissolve, say 30 frames (one second) in duration. Since the dissolve is centered on the cut, it will start 15 frames before the cut, and try to go 15 frames AFTER the cut...which it can't do. What you need to do is plan how long your dissolve will be and back-time your cut so that it works.
You need to make sure that your clips have enough media (called 'handles') at the beginning of the incoming clip and at the end of the outgoing clip for the transition. For example, if you have a 1 second (30 frame) dissolve, your in and out point need to be at least 15 frames from the edge of the clip.