Are my brakes too close to the rim? I like having my front brakes very close to the rim (see image) as it makes it much easier to brake, especially when on the hoods or long descents.  I recently swapped to Continental GP4000 25mm tires on Mavic CXP 22 rims and the tires seem to be much wider than my previous stock Felt All weather 25 mms.  When I want to take the wheels off, I need to loosen the brake cable in addition opening up there brake calipers. This is of course very annoying and seems abnormal to me.


105 shifters
Shimano calipers with no model number
From the picture, and what you describe, the tire is wider than the rim. This means that if you like to run the brake shoes close the rim that you'll be unable to remove the tire without having to find some way to "lengthen" the cable. There are three common options that I know of:


A release lever on the brakes. It appears that you have one. I think that is what the silver lever on the left side of the photo is (near the brake cable). If you lift up on it, the brakes should relax enabling you to remove the wheel.
Some brake levers will have a button to release cable tension. My Tektro levers do, My Shimano levers don't.
There may be a barrel adjuster screw on the brakes or levers someplace. The primary purpose of this is to let you tune the length of the cable, but it will also give you a way to release some cable tension (if they are screwed out some). Not ideal, but better than unscrewing the cable clamp.