Hi,
What is the meaning of this phrase?
I looked it up in Garner's usage book and it says "if you will" is an elliptical form of "if you will allow me to use the phrase". Then, what does "if you will allow me to use the phrase" mean?

He doesn't provide an answer to that. So, I did some searches and found some other explanations for this phrase.
<New York Times>
"If you will" is a shortening of "if you will permit me to say" or "if you will pardon my saying so," which is not quite what the clipped phrase means. The speaker or writer needs no such permission; on the contrary, the shortening means "I'm going to say this, and you may not like it, but that's just too bad, so here goes." The point is not to show deference, as the words say, but to make a pass at submissive respect while making a forceful point.
<Geoffrey Pullum(one of the authors of "The Cambride Grammar of the English Language">
1. like
Geoffrey Pullum has noted that "if you will" can serve the same function as the much-maligned discourse particle
like: "a way to signal hedging about vocabulary choice — a momentary uncertainty about whether the adjacent expression is exactly the right form of words or not." Semantically it does exactly what
like does.
ex1)
A: They are, if you will, this country's governing body
B: They are, like, this country's governing body.
ex2)
A: We were willing to overlook it, if you will, being a growth company.
B: We were willing to, like, overlook it, being a growth company.
2) concession
Beyond that sort of hedging, "if you will" and its phrasal kin ("so to speak," "as it were," "if you like") may be doing other pragmatic work, such as "making a concession… without commit[ting] the writer or speaker to that position fully" ( He doesn't give any examples of this use)
Okay, it's now time for me to ask questions.
Q1) As for the New York Times' explanation, I couldn't understand the gist of what the author wrote because of the last part. "The point is not to show deference, as the words say, but to make a pass at submissive respect while making a forceful point." What is the author trying to say here? Could you give me an example?
Q2) ""like" is a way to signal hedging about vocabulary choice—a momentary uncertainty about whether the adjacent expression is exactly the right form of words or not."
So, this means that whatever comes after "like" conveys the speaker's lack of confidence about whether it's the right word choice? And "like" or "if you will" plays a hedging role in a way that the word that follows it may not be the most appropriate term. Correct? (I hope you understand what I mean)
Q3) "if you will" and its phrasal kin ("so to speak," "as it were," "if you like") may be doing other pragmatic work, such as "making a concession… without commit[ting] the writer or speaker to that position fully"
It's not clear what he means by this. Could you explain and give some examples?
I'd really appreciate it if you could take the time to answer my questions.