I agree that if you're being given responsibilities you really don't feel capable of meeting then it might be a question of judgement regarding the teacher. Alternatively, he or she *could* be giving you a 'stretch target', that is, making you reach for something you don't think you're capable of but the teacher thinks you really are, if you are given the responsibility. Another possibility is that you're projecting what you think is the responsibility based on your idea of what the practice represents.
So - without further information, it is very hard to say. But remember the meaning of 'responsibility' entails 'what you're able to respond to'. And the basic responsibility for any person, anywhere, always comes down to doing your best. Nobody can ask more of you than that.
Learn to do good, refrain from evil, purify the mind ~ this is the teaching of the Buddhas