I don't play the clarinet, but many beginner flute players find it difficult to hold a note for more than a couple of seconds - doing separate breathing exercises can speed up this process (as can the amazing pneumo pro!) Many older children and adults don't have a problem with this, so the exercises aren't necessary.
I do agree that it is best to discuss concerns with your teacher. Learning an instrument should be done as a partnership with the teacher as a guide. Teachers do usually (I won't say always because in any profession there are going to be a small minority who don't do a good job!) know the best way to learn and most of us have spent years both mastering the instrument ourselves and then learning how to teach others. However, it is important for both the pupil and the teacher to know what they want to achieve from the lessons and for the pupil to understand why they are being asked to do certain things so they are able to practise them properly. It is the same in schools - children are given the learning objective for lessons, along with more detailed lists of outcomes they need to achieve. Long notes are a good example of this - too many children just play each note without actually listening to the quality of sound they are making, or trying to make it longer/louder/quieter etc.
It is also worth noting that teachers will teach things in different orders for different pupils, depending on prior knowledge, age, natural ability and so on. There is no one correct method.