When you play the clarinet, breathing takes a few more things into account beyond the principals of how breathing works.
Click here for tips on the basics of breathing
Click here for clarinet breathing exercises
When you take breaths, simply expand the corners of your embouchure outward, keeping your top lip on the top of the mouthpiece.
When you lift your top lip off the mouthpiece to inhale, not only can you not get in as much air as your would through your corners, but it also takes more effort to reset your embouchure. This is especially true when you have to take a quick breath.
Take a piece of paper about 1 X 1", stand close to a wall and try to hold the paper onto the wall with just your air. Notice that your airstream has to be very fast and constant to keep it on the wall. This is clarinet air.
Hold your hand about a foot from your face and blow air onto the palm of your hand. Aim your air straight ahead and speed it up so that it feels cold on your hand. This is also clarinet air.
Fog up your window with your breath. It is warm and slow to get the condensation. This is not clarinet air.
If you have a weak, slow, inconsistent airstream, fast and consistent air will improve everything about how you sound, including tone quality, articulation, intonation, phrasing, large intervals and dynamic ranges.