Why can't we target fat loss?

Fat loss is a global process. That is to say, when you train, you lose fat all at once from all over your body.
Why it tends to stick around in certain places longer than others is based largely on your genetics as hulk pointed out. Building muscle is different, as muscle is a permanent and adaptive biological structure. It is supposed to be there...excess fat is not.

If you have hit a plateau in your fat loss, it might be time to change things up. Heavier lifting, more reps, different exercises, etc;. Any new stress that your body has to adapt to can help ignite your fat burning furnace.

No. YOU have no choice in where your body loses the fat first. Just ask my boobs. Went from DD to an A before I got rid of ALL the tummy fat LOL

'cuz of science and stuff

I was somewhat surprised to find out recently that you can in some ways target fat loss.

Studies have shown that High Intensity Interval Training (HIIT) is not only great for lowering overall body fat, and in less time than standard aerobic exercise, but it is particularly good at reducing abdominal fat. Here are two such studies:

http://www.nature.com/ijo/journal/v32/n4/abs/0803781a.html

http://mobile.journals.lww.com/acsm-msse/_layouts/oaks.journals.mobile/abstractviewer.aspx?year=2008&issue=11000&article=00001

And a recent study into body composition of (female) marathon runners vs. ironman (woman!) triathletes had some interesting findings:

http://www.ncbi.nlm.nih.gov/m/pubmed/23347010/

I'm not sure if the marathon running vs ironman triathlete study has been replicated, I'm guessing not, but the finding that HIIT preferentially targets abdominal fat loss has been replicated numerous times.

I keep hearing that our bodies lose fat when and where they want to, you can't target where you lose the fat from first. Which is really frustrating. By doing "targeted" exercises, why isn't it possible to get rid of fat in those spots?

Sadly it's a design flaw! Sort of like asking why we can't grow a third arm if we really really want to.

As an apple I feel your pain.

But, while it isn't possible to target where the fat comes from it is possible to target where muscles are built so maybe focus on that. Then as the fat does slowly come off you'll be really ripped underneath.

A few studies have found that HIIT can hit visceral fat more efficiently than steady state cardio, this is another one:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2991639/

BUT unless you're in top-top shape, it's really hard to find a way to fit it in with strength training & get enough recovery & not risk injury.

And strength training's good from a body shaping point of view, because that's where you can a *little* more selectively build up bits under the fat & look solid. It's good from a health point of view because it helps prevent osteoporosis and other ailments.

I think regular resistance training + some moderate cardio is probably safer & more effective for most people who aren't male 22-year old athletes.

Yes, safety can be an important issue. I am a long distance runner (I'm not on MFP to lose weight) and I only do one HIIT session per week. The following day is usually cross training or active recovery. One doesn't have to be running, though. You can do it just as well on an elliptical machine or stationary bike which, being lower in impact, may be better options for those who are injury prone. I'm somewhat prone to injury, but whenever I've been injured it's been from ramping up my kilometers too quickly, not from doing speed work.

I don't think that HIIT should be considered purely the domain of young athletes. The studies have focussed predominately on obese individuals, and it's frequently prescribed along with other cardiovascular exercise and weight training for people pursuing weight/fat loss. I would thoroughly recommend it, but it is important to build up some base fitness first and obtain medical clearance if you have / might have any health issues, e.g. heart, as should be done before starting any exercise. These are truly lung busting efforts when done correctly!

So people train the top and bottom of their body, but some people neglect

Mainly cause your body is smart at hiding fat out of your reach damn you genetics