Is it possible that some people just can't get abs?

What body fat % should men and women aim for if they want visible abs? I don't really have a means of measuring body fat, but I know there are scales with metal foot prints in them that claim to measure it. The lowest body fat I've been (That I know of) was 18.5% because a health group came to my school and put my finger in some sort of clamp thing. That was the year I was training a lot in kickboxing and jiu jitsu.

I think for women the possibility starts around 19%, and will depend on how you carry your fat. If you're someone that carries your weight in your midsection, you may have to go quite a bit lower.

ETA: to the original question, I think it's technically possible for everyone, but may not be worth the sacrifices necessary for a lot of people- women in particular. I personally would not be willing to go so low BF% that I give up my curves to have visible abs.

Where does the quest for visible abs end and the journey into anorexia begin?

It's rare to see people with decent muscle be criticised as being 'anorexic' - but to be fair I'm probably more thinking the sort of Abs I want ('man abs', what with being a man ), while a lot of women would prefer a bit softer, just showing 'a bit of tone'.
I find it hard to believe that people couldn't get visible abs - everyone has the muscles and I can't believe if someone did a decent bit of exercise, then 'cut' to 6% body fat (for men, equivelent for women whatever that is) that they wouldn't have visible abs.

Depends a lot on how your body fat is distributed. I had a ton of abdominal fat when I started getting in shape, and it takes forever for guys to lose fat there, so I didn't start getting good visibility til around 10%, and even at 7% still had some fat on my lower abs (bottom 2 of six pack not clearly defined unflexed), despite visible chest/shoulder striations (which is total BS). I think one more round of bulking and cutting should get me to having a nice even body fat distrubtion, but this has taken a couple years of effort.

TL;DR: The quest for abs is like the search for the holy grail... difficult, but once you find it, you will LIVE FOREVER.

...ok, maybe that was a bad analogy.

I don't know.... my belly always has definition but not abs. Sort of like this -

Its possible for all, but more difficult for some. Its a combination of fat mass over the abs and muscle size.

You can have very little fat but not have visible abs due to lack of muscle mass. In the end, its possible, but more difficult and time consuming for some. It took me the better part of 2 years to lose 150 lbs and see my abs. And I once had a 60+" waist.

So if I can do it, anyone can with the right amount of dedication and willpower and knowledge.

Very few people (maybe none) will have their bodyfat equally proportioned over their entire body. That is why the most accurate caliper measurements involve testing many sites over the body. So obviously the overall BF% to see visible abs (or ripped biceps etc) is going to vary from person to person, depending where their bodyfat happens to deposit. For me, I reckon I'll see a 6-pack before I'd see really lean sculpted arms and I'll never see a "thigh gap"...

A couple thoughts I have on this subject as one who has a somewhat visible six-pack but not cut to the point that I'd like.

First, genetics: Different people put on fat differently. For most men their most stubborn fat (i.e. the last to go) is in the mid-section right around the very ab muscles we're talking about. For most women it's their thighs. However, this varies quite a bit.

Second, Body Fat %: The numbers I've read in many places for when Ab muscles start to show are 9% and below for men and 15% or below for Women. Again, the above consideration about genetics will affect this. In my experience with my own body, 9-10% is about where I start showing.

Third, Age: One thing I haven't seen mentioned here yet is age. As we get older it gets more and more difficult to get that chiseled or shrink wrapped look that is needed to get those model abs we see in all the pics. Skin becomes less resilient and adipose tissue (fat cells) tends to become "looser" as well.

Fourth, Skin Resiliency: As I said already, age can affect this. So can the amount of weight you were carrying before you lost it as well as how long you carried that excess weight. Especially in women this can be particularly problematic in the belly area. Skin just doesn't always return to it's previous state. Loose skin can make it much harder to get your abs visible. Things like smoking, excessive sun exposure and such can also impact your skin's resiliency.

Fifth, Muscle Mass: As you shrink down and loose the fat in your mid-section, you need the muscles behind it to have sufficient mass to become visible. The more mass they have the easier they will appear. Loose skin from weight loss requires additional muscle mass to compensate. It's easier for men than women to produce the type of muscle mass needed in most cases. Regardless if you're not doing strength training, in particular including movements that target your abs, your success will be limited.

So no, I don't think it's impossible for anyone, however there are a lot of factors that are common for many people that can make it much more difficult. So for some people it may be next to impossible and would require significant effort above and beyond the already difficult task of getting rid of the infamous last 10 lbs.

** EDIT ** If you want some additional information to help explain why it is so hard to lose that stubborn fat and give you some ideas to help, I really enjoyed Lyle McDonald's book "The Stubborn Fat Solution". I'm not following his protocols yet, but just the information he gives you is extremely helpful in terms of understanding why your body is doing what it's doing.