The only way to lose weight quickly is to fast.  Your body will consume its
muscle.  The heart is muscle.  People who die after fasting or starving
themselves tend to die of heart attacks.

The way to get healthy is to exercise, including aerobics, and to eat
limited numbers and sizes of portions, of a wide variety of high fiber low
fat food.

The simplist observation is that more folks who lost slowly
manager to keep it off and more folks who lost slowly regained
quickly.  With money it's "easy-come, easy-go", with fat it's
the other order.  Since yoyoing is worse for health what
counts in the long run is keeping it off so any strategy
that increases the chance of keeping it off is preferred.

On the research side look for lean loss and fat loss
compared to loss rates.  Fast loss is nearly always
associated with greater lean loss and slow loss is more
often associated with fat loss.  The goal is *weight* lost,
but if you step back and think about it for a while that's
not right.  The best goal is *fat* lost.  Losing lean is
bad.

There's an evolutionary reason that fast loss tends to be
the body canabalizing its own muscle and hoarding its fat.
Our ancestors experienced famine after famine.  When a
famine starts there's no way to tell if it will be a short
one or a long one, so the body assumes it will be a long one.
Fat stores are needed to survive long famines so they are
kept in reserve instead of used immediately.  Muscle tissue
burns fuel much faster than fat tissue so in the early phases
of a famine the body reduces muscle first to reduce total
energy needs.

Modern diets never move the body past those initial muscle
loss phases into the fat loss phases.  That's not dieting;
it's anorexia when done on purpose.

So the trick on a modern diet is to use skill to get the
body to drop fat instead of muscle early on.  The way to
do that is to lose slower than would happen during a famine.
This is why the best low calorie programs are mildly low
not very low in calories.  This is why low carb plans
aren't ever low protein.  This is why good low fat plans
keep protein and fat levels up above a minimum.  They are
all intended to prevent this "starvation mode" where the
body tries to reduce energy needs by cutting metabolism and
canabalizing muscle.  And they all depend on a loss rate
that all new folks find frustratingly slow.

Everyone who's ever started a diet hates to lose 4 pounds
per month, 1 per week, but losing faster than that risks
losing muscle rather than fat, and losing muscle triggers
rebound hunger and rebound gain.  And the faster you lose,
the more the risk.

As frustrating as it is, slow loss is safer and lasts longer
than fast loss.

There are more reasons -

Vitamins, minerals and so on.  When losing fast it is much
easier to become deficient in various nutrients.  While
there are ways to handle this they require plenty of
attention.  Attention comes from a carefully designed
program.  Carefully designed programs take muscle vs fat
loss into account so they don't target fast loss.
Therefore folks trying to lose fast don't have these
carefully designed programs to cover deficiency topics for
them.  The extra work of cutting for fast loss plus careful
counts of nutrients isn't something that most fad dieters
making up their own plans think of doing.

Toxins stored in fat.  Many toxic substances are fat
soluble and the body is evolved to isolate toxins away
from the rest of the body.  Toxins end up getting stored in
the fat.  Lose that fat fast enough and nasty stuff comes
out into the blood faster.  Folks losing fast get all sorts
of minor symptoms from pimpiles on sometimes because of this.

Given time I could think of other reasons that slower loss
is healthier.  Every reason would add to the frustration of
folks wanting to lose fast and there's no way around that
frustration but to go through it and come out the other
side a couple of years later.

Another reason is that to lose weight quickly, you have to go through severe
caloric restriction. It's very difficult to eat bellow 1200 calories and to
maintain a proper micro-nutriment intake. If you don't take that into
account, it's easy to end up with a severe mineral or vitamin deficiency,
which can have some very very severe consequences. Like, I saw on TV a woman
who had  osteoporosis because of her "protein fast" diets, at barely 40...
Your body needs vitamins, minerals, oligo-elements, essential fatty acids...
That's a lot of supplements to take if you don't get these through foods.
And many supplements are bad quality (they chemically contain these
nutriments, but in a form the body has a very hard time assimilating). Also,
the body has a hard time using some of these if it doesn't get some fat from
the food (all fat solubles vitamins, some minerals like calcium). Finally,
very low calorie diets often use a *lot* of non-soluble fibers to create
some volume. Non-soluble fibers are not the best (soluble tends to be
better; they make a better job at slowing carbs and give better protection
from cancer). Too much fibers can flush vitamins before you get a chance to
assimilate them.