It was my understanding (and maybe this is incorrect) that someone only remembers their dreams if they wake up during them. Therefore, not remembering them could just be a sign you've had a good, uninterrupted night's sleep. Anecdotally, this seems to be the case for me–I remember my dreams if I'm woken up e.g. by a car alarm but never if I wake up normally.
I've always been told that you have to practice remembering dreams in order to get better at it. And the often-cited way of practicing that is by keeping a dream-diary that you're suppose to write in whenever you wake up.
Likewise, I've never heard of the whole "you only remember a dream if you wake up during it". Sometimes I go through a few dreams, wake up naturally, and remember some of the previous ones (and not the last one).
I too thought this was the case. I very rarely remember what I dreamt last night, it may happen once in five months if I'm lucky. But I always thought that was perfectly normal.
It was my understanding (and maybe this is incorrect) that someone only remembers their dreams if they wake up during them. Therefore, not remembering them could just be a sign you've had a good, uninterrupted night's sleep. Anecdotally, this seems to be the case for me–I remember my dreams if I'm woken up e.g. by a car alarm but never if I wake up normally.