Ok, I grabed my cat and made a quick drawing to show you what I was trying to say before:
(My apologies for the bad quality, not the best scanner)
Step 1 (~5mins)
First of all I sketched the outlines of the overall shape, (i started with the circle that will be the head). Then I made soft inner outlines of the legs and up to the root of the tail. I also added a mask for the facial features. The ears are pretty easy (for me) so I did them already.
Note: No details at the beginning, keep it simple, keep it 'ugly'
Step 2 (~6mins)
Added first sketch of facial features, corrected and solidified outlines, added a few details. Look at the hindleg (if it's possible to tell where it is

). It's very shaky, it has no definite outlines, you can still see that I first drew it far too short (twice). I was more or less satisfied with the third iteration.
At this point the face creeped me out, because it didn't look anywhere near good, so I erased it softly, so I could still see where my former lines were. With that shimmer of a line I redid it and I was still creeped, because it still doesn't look as good as I wanted it, but I left it at that.
Note: You need to tweak your details. Never assume you get it right at the first try. Redo lines over and over until you are satisfied (erase if they get too bold). It's hard to keep going, because it just doesn't look like you want it to be. But hang in there, it will get better.
Step 3 (~14mins)
Added first fur, Whiskers and eyes.
It's pretty challenging to draw fur in greyscale...

, specially if the hairs have different lenghts. After I added the actual eyes, the face looked much better. You may notice that some lines in the face have gone less bold, that's because I had to erase it again. (I think faces and eyes specially are one of the most difficult things to draw realistically). I also bolded some details.
Note: Details are the flesh on the bone of your sketch. But beware: don't overdo it, because it might look weird.
The "final" version (~5mins)
I added some shading (hard to see on the scans) and more fur, replaced outlines to look furish
I wanted to finish the drawing at this point, because most things I wanted to point out were allready included and because it's almost 2 am.
I'm more or less satisfied with the outcome of my 30 minute drawing (considering the difficulty of the object). There are some things I don't like about the drawing which I'd change if I continued this piece.
I hope it helped.
I don't think anybody just can't draw by default (except they have no hands, feet...mouth?....a******

), it's just the lack of technique and patience that makes it so hard.
Disclaimer: I don't say my technique is entirely flawless. It probably doesn't fit other people and it should not be taken as the ultimate truth. It's just the way I think it's easy to get something decent without despairing.