This is mine so I am not sure if it's what you are looking for.

People who take Government handouts are Moochers.
Ayn Rand accepted Social Security and Medicare.
Ayn Rand is a Moocher.

I hear this from Rand haters from time to time.

It can't b true because "I never heard of it."

By taking money for enough hammers, some gangs think they can stimulate the economy of any town.

Equivocation is most probably the funniest...

Only solid objects may strike me.
Lightning in not sold.
Therefore, I cannot be struck by lightning.

While not actually a logical fallacy, that certainly a good example of collectivist thinking.

Ad misericordiam: This argument must be valid because there is suffering. As in "You must give up some of your property because that person has none of his own".

There were some screwy Roman philosophers. One of their favorites:
Post hoc, ergo propter hoc.
I was going to leave it un-translated, but that's not playing fair.
"Following this, therefore because of this."

My favorite logical fallacy?

Argumentum ab auctoritate ("It's true because the best professors of economics say so!")

And its close cousins:

Argumentum a gradis (literally, "from one's grades". The form of this is: "How dare you criticize a person of my talents? Look at my grades, and look at your grades, and let's see who's qualified!")

Argumentum a populo (argumentum a numeris, argumentum a multitudine): "You're in the minority. The majority can't be wrong." As if truth were subject to a vote.

I hate them all but my least hated, and I guess my favorite, is: equivocation. Normally those are easy to point out and correct.

Yes.

"There are two sides to every issue: one side is right and the other is wrong, but the middle is always evil." Ayn Rand

Ditto.

Appeal to the expert. If a smart person says it, it must be right, without logical support.

My favorite one is "middle ground." IMO, there is no nobility in "reaching across the aisle" when it results in surrenderihng freedoms or wrecking the economy (that includes ditching jobs for the "climate change" we've always had). And try to seek "middle ground" with a Muslim suicide bomber who will kill you for not converting from Christianity or for being born a Jew.

False Alternative is mine as well

Henry Hazlitt's "The Broken Window Fallacy"...seeing only the immediate effects and groups' impacted by government policy while ignoring long term effects and other groups involved.

"on a pedestal" like doctors, priests, presidents, etc., etc.

Favorite as in most annoying: False Alternative.
As in most serious: Misericordium - Appeal to Pity, because it is such a part of Altruism.

"Governments = Roads" {sorry}

When you say 'favorite"...???

But I would say: Argument...
from ignorance
from silence
to moderation

This doesn't really go along with a John Galt theme, but one statement that is a logical fallacy is: "This statement is false."

;) - at least that leads to a civilized exchange, if not logically rigorous...

Confirmation bias. Yup.

It's not really a fallacy, but one of the worst reasoning errors that comes natural to us all is to pick a conclusion and then look for evidence to support it.

My favorite fallacy name is the "no true Scotsman" fallacy, which is a form of special pleading.

Too often I rely on my own experience. This falls under the anecdotal fallacy.

You find many of them here in active use. We just prefer to be polite to each other.