When I started I could never understand why either: my legs packed up while my breathing was ok, or my breathing packed up while my legs were fine.
At some magic point--after weeks of not being able to do more than 10 mins a time--you suddenly realise WHOO HOOO!!! I CAN RUN! I CAN DO IT!!
The next day, of course, you couldn't make it to the corner shop if you had a gun to your head.
This is perfectly normal. The knack is to find something interesting to think about, not worry too much when bits of your body stop working (stopping to tie your shoelaces and gasp for breath is ok, and so's walking) and just, basically, to get on with it. Because nothing, absolutely nothing, compares with the quiet satisfaction of knowing that you can, when you feel like it, head out for a nice six mile run . . . or ten . . . or twelve . . .