Not in Spanish (el gato) or French (le chat).
Your ideal dog (in that platonic form sense) is territorial, playful and aggressive – all stereotypical male gender attributes. It’s also larger than your ideal cat. Since both animals occupy much the same purpose and mental landscape, and we begin to understand these independent entities pretty much the same time we begin to understand the difference between the sexes, we sort the animals at the same time.
Similarly, your ideal cat is affectionate, languid, and fastidious - all stereotypically feminine traits.
This is an excellent point, and probably goes a long way to answering the question.
I’ve wondered about this for a long time. In fact, I have a distant, perhaps imagined, memory of being in pre-school and whatever the equivalent of the old Dick-and-Jane was that we used had a picture of a boy with a dog and a girl with a cat. Being, at the time, of an age when gender roles first become noticed, I remember feeling vaguely uneasy that my own preference, cats, was associated with the girl.
In fact, in the actual Dick and Jane books, Dick had Spot, the dog, for a pet. Didn’t Jane have a cat?
Despite the fact that I remember wondering about this as a small child, I don’t think I’ve ever put the question into words, or even been sure I was observing a real phenomenon. When I saw the question posted, I immediately knew what was meant, but I was a bit surprised to see that someone else had noticed it.
BTW, it is perhaps worth noting that although dogs are almost always presumed male, there is one exception: the poodle. Not only are poodles seen as female, depicting a dog as a poodle is shorthand in almost every animal comic-strip or cartoon for showing a female dog.
Also, although cats are presumed to be female in many contexts, “tomcatting” is used to describe prototypically male behavior. And although men are often called “dogs” (either negatively or positively) it is far more common to hear a woman called “bitch” (always negatively).
Fluff. Why I remember this after fifty years while being unable to recall the names of people I met five minutes ago is one of life’s great mysteries.
Take solace, because I don’t think Fluff was the name. I think it was Puff.
See? You don’t remember anything! Isn’t that better? 
I’ve just finished reading a handful of articles about the Victorian science and politics of the human body. A common concept that is often highlighted in anatomical descriptions of that era, which (inevitably) compare men to women, is the idea that women are physically more delicate than men – finer bones, finer features, less strength, smaller stature, etc. Some anatomists went so far as to feature a suitable animal skeleton posed next to a human skeleton in an attempt to highlight sexual differences. For example, I noticed a drawing with a male skeleton posed next to a horse (a stallion, of course!) while the female skeleton was posed next to a bird.
In short, the matching up of sexually dimorphic traits in humans with particular species of animals has not only a popular but a “scientific” tradition, and it may be part of what’s behind the idea that cats are feminine and dogs masculine.
Rats. I even did a Google search to check on it. At least a lot of other people misremember it too.
I should have recalled the National Lampoon parody on Dick and Jane, where Puff’s name came into one of the jokes.
[spoiler]
From National Lampoon’s Dick in Jane
See Spot.
See Spot hump.
See Spot hump Puff.
Hump hump hump.
Puff puff puff.
Come Spot come![/spoiler]
Whence the notion that cats are “she” by default?
Answer No. 1: Since tomcats are males, cats ought to be she
Answer No. 2: Since a cat is a pussy, it’s got to be she
Answer No. 3, and the correct one suggested by Thudlow Boink: a legacy of German die Katze.
Why do you believe that is the correct answer?
In French, and I think all other Romance languages, the word for cat is masculine.
Interesting idea, but we don’t do this with geese and ganders, do we?
I think we’d have to explore the origins of the various usages of ‘pussy’, and which came first. Did ‘pussycat’ come before ‘pussy’ meaning ‘weakling’ or ‘vagina’?
Just to be clear, in mentioning grammatical gender, I was referring to Old English, which presumably had the same gender for ‘cat’ as German does for ‘Katze’ today.
No, there are usually up to four males to the pride, and there are also nomadic males who haven’t managed to get into any pride at all. Wikipedia’s article on domestic cats doesn’t support the assertion that most cats are female.
Pussy galore?
^ ^
In French some animal names are feminine:
une girafe
une antilope
une loutre (otter)
une souris (mouse)
une gerboise (gerbil)
…
most other animal names are masculine
When names are masculine, there’s often a feminine for the female, especially domestic and some popular animals:
le chat - la chatte
le rat - la ratte
le boeuf - la vache (ox - cow)
le bouc - la chèvre (billy goat - nanny goat)
le porc - la laie (pig - sow)
le cochon - la cochonne (pig - sow)
le cheval - la jument (horse - mare)
un âne - une ânesse (donkey)
le lion - la lionne
le tigre - la tigresse
some don’t have a feminine:
un zèbre
un gnou prononced (g’noo)
un écureuil (squirrel)
un spectre
un pithécanthrope
and most lesser known animals (don’t be vexed 
)