Animal fats aren't better, they're just not worse, but the caveat is
that they're not healthy unless they come from grass fed animals.

I would be cautious about eating Omega 6 laden oils, and grain fed cows
are overly high in 6s and other pro inflammatory substances, too.

Susan

I suspect the statement was while on low carb fat is superior
to carbs and thus there is no reason to fear animal fat.

I figure there are cases who have problems converting plant
fats into their own fats so they'd do better with some animal
fats - Consider statements that people with a certain fraction
of Celtic or NW Native American blood should have fish oil
rather than flax seed oil.  But this seems an edge case to me.

Generally, calorie for calorie, gram for gram, there is little or
not down side to draining off animal fat and replacing with
plant fat.  The thing is there's also little of no down side to
keeping the animal fat and ignoring the plant fat.  Animal fats
have plenty of essential fatty acids so it should matter little.

If your plan says to do that, then do that.  The authors of the
popular books put a decade or more of effort into their books
and that includes optimizations that are not obvious.  Take
advantage of their work by following their directions including
the parts you disagree with or don't understand.

I think its amount of essent fatty acids or ratio of essential
fatty acids.  Consider the usual spectrum ranging from good
fats through bad fats -

Extremely good fats - essential fatty acids as found in
animal and plant fats.  Omega 3 and 9 in various ratios and
with fatty acids whose chains are in various lengths.

Very good fats - monunsaturated fatty acids can be burned
for fuel, can not be converted to other type, can not be
stored.

Good fats - saturated fatty acids can be changed in length
to become human ones, can be synthysized by the human
body, can be burned for fuel, can be stored.

Bad fats - transfats.

So why would a plan suggest plant fats?  Either because
they have studies and data saying it works better, or
because they get less heat if they include it in their plans.
Folks do remember how much flak Dr Atkins took and no
matter that he was right and the anti-fat brigade was wrong
he is now head no longer leading a crusade.  Plans that
do not fight that battle do well avoiding that combat.

Calorie for calorie, gram for gram, is animal or plant fat
better for loss?  It's possible to locate studies that say
plant fats work better, but these studies are rare enough
they are poor evidence.  It really looks like there's no
difference.

Calorie for calorie, gram for gram, is animal or plant fat
better for health during maintenance?  You could look to
paleolithic eating plans for suggestions on why to think
animal fats are better, but again I see this evidence as
weak and contrary to my mention above of the rare studies
that suggest the opposite during the loss phase.  It really
looks like there's no difference.

Calorie for calorie, gram for gram, is animal or plant fat
better for public relations?  There is an *enormous*
difference in public perception.  Right or wrong I suggest
this is the strongest reason.

Yes. Animal fats are healthier. Lard, tallow, chicken fat, etc. Also
real butter, real whole milk without excessive pasteurization and
homogenization. Second best is evoo.

Stay away from highly processed fats like canola, soy oil, margarine,
shortening, etc. The less processing the better.