How can my cat be so extreme?

I have always had cats and been passionate about them. I adopted my
current cat from a vet where she was being given away free from a
litter that came unexpectedly to an old couple. She was only 3 months
old, and timid from lack of interaction. I was concerned that she
might always be skittish, but she enjoyed being petted and warmed up
to me with effort and patience.

This cat has been an ideal cat for a small apartment because she is
proportionately small, doesn't chew things or knock things down or
lunge for/break into food left on the counter. Best of all, she's
content with one room and doesn't even try to make an escape when the
door's left open. In short, she's exceptionally mild mannered.

I'm accustomed to most cats natural vehemence toward other cats when
they haven't been around them much. And I've heard many a raucous cat
fight. But I have never seen the like of this normally timid cat when
she goes berserk. I first met this side of her when she caught sight
of an outdoor cat for the first time, but thankfully she has become
more accustomed to it and toned down.

Today, however, I fraternized with one of the outdoor cats. When I
came in, I petted her with my foot until I had washed my hands
thoroughly, but when I reached out for her she detected something and
reacted toward me exactly as if I were a vicious predator who'd just
taken a bite out of her. Hissing, snarling, and growling like I've
never heard and can't adequately describe. It was like she was
rabid. She lashed repeatedly and drew blood. I actually had to fear
her; I thought she'd claw my eyes out if I came to close. I had to
put on some gloves to pick her up by the scruff and put her in the
bathroom (which is punishment for bad behavior). She didn't remotely
calm down while she was scruffed. She was so upset to have my hands
on her that she peed and defecated while growling.

I left her alone for a while but when I went back she got worked up
again. I feel like I'll have to take a shower before she treats me
like the person who has cared for her for most of her life.

This behavior seems seriously excessive. It feels terrible to be
treated like an enemy by an animal I've done nothing but love. Has
anyone else experienced the like? I don't know if I can keep this up,
when she's like this.

Seriously, my cat is psycho. After leaving her in the bathroom for a
while, I went and washed my hands and arms and changed clothes and
then tried petting her. She reluctantly endured it for a minute and
meowed in a calm tone. She sniffed me extensively, and then
apparently suddenly sensed something she still disapproved of and went
back into hysterics. I was so disgusted I decided to set her up with
a box in the back yard (it's fenced) to give her some experience with
alien smells.

After about 30 min I went to check on her. She was laying with her
head and paws outside the box. She meowed familiarly when she saw me,
then about ten seconds later put her ears down and backed away from
me, hissing and growling. I hadn't even moved. This is crazy!