1yr old doesn't seem to love us

Hi,
Me(29) and my wife (35) have a beautiful "patched cat" that we love very much. She's cute and we give her a lot of affection but... She doesn't like our company so much we think. Why ? read on:
- She never comes to us when we're on the couch or the bed to play, cuddle or to be touched even.
- Whenever I approach her she goes away, or never lets me stroke her more than once
- The only time that she allows us to cuddle her is when she wants food.
- She wakes up my wife every morning at around 6u30 because she wants food and won't eat unless she stays with her.
- She stays on the window the whole day behind the "flyscreen" watching the birds, goes from one window to the other and just sleeps the rest of the day (we have an appartement without garden, sadly).
- She won't let us hold her for more than 10 sec before pushing us away.

It's like we're complaining now, but we're worried that she's not happy.
She's a very good cat in the way that she doesn't use her claws on our furniture, never...
Sometimes I think that we got her too early (6 weeks old) and that she
now has some character flaws, but she's actually ok with other cats (when she's done with blowing and guarding territory for 2 days or so).

Is there anything you can suggest to us to improve our relationship with our cat?

P.S.: we got her sterilised, and she has a lot of toys and a big climber.

Some cats are just more independent then others - you have one. Adopting at 6 weeks could be a factor - poor social skills. I'm assuming she's an only cat? That could make it worse cause no one taught her how to be social.

Tho some will say it doesn't have anything to do with it, the fact is she IS a female and IS tortie (multicolor) - torties tend to have more of an independent attitude and are less social. Yes there are exceptions, but most of my torties/calicos were less friendly.

Male cats (neutered) usually are a lot more social, loving, lap sitters. Perhaps you can adopt a more outgoing young male kitten (4-8 months old) or even a laid back, lap cat male a few years older then your female?

Hey, thanks for your reply - this was helpful!
Especially because a few months ago we had a young male british shorthair over
for 2 weeks, because the owner went on vacation.
I remember that I enjoyed his company a lot because this kitten was very playful and liked our companionship also.
The only thing that bothered me about this brit shorthair was that he smelled bad from his mouth.
Is that a typical thing for these cats?
Thanks a lot!

Do you have any interactive toys? I find playing with Sophie is a bonding experience.

Does she like to be brushed? Grooming time is another way we bond.

When she does let you pet her, maybe you can give her a treat afterwards and see if that makes her more receptive to you.

Shouldn't have bad breath at a young age. Does this cat eat a lot of fish?

I don't know if his breath still smells, I haven't seen Achilles (his name) in
quite a while now. I'll ask the owner if I see her.

I'll try the petting/reward thing and see if it works.

She does come to me for about 2 sec. when I'm at my desk and I call her
and put out my hand, she does the headrub with my hand and goes...

She does like to be groomed, so I'll do that a little more.

Thanx for the advice!

I'm glad she likes to be groomed! Sophie likes it so much that if I just call her name and show her the flea brush she comes right to me. When I'm petting her, I just say her name and tell her she's a good girl. And I make eye contact so she knows I'm paying attention to her. It's really a great experience, and I can tell she enjoys it, too. Good luck!