What kind of rhetorical strategy is it when someone points out a potential sticking point in his proposition before anyone can criticize it?

E.g.:

• I know some of you might consider this question general reference, but think of all those people who will be reading it all over the world and how it will enrich our data bank.

• Of course we all know how expensive it would be to build new headquarters for our institute. But think of what is going to happen to our research center and our reputation if we don't

Edit - changed "fallacy" to "rhetorical strategy"

That's not a logical fallacy. It's a very common rhetorical tactic called procatalepsis, or more colloquially in American English, prebuttal.

The strategy consists of anticipating your opponent's argument, and then responding to it, as if they had raised the objection themselves. That way, they can't later raise that objection, because you've already done it for them and explained why that line of thinking would be wrong.

Of course, the way in which you respond to the argument may contain a logical fallacy, but that's a separate issue from the fact that the rhetorical strategy is being used at all.

It's not a fallacy. But you could call the rhetorical technique a stratagem.

an artifice or trick in war for deceiving and outwitting the enemy

skill in ruses or trickery

Dale Carnegie proffered this stratagem in How to Win Friends and Influence People.

In "Be a Leader," points 8 and 9 are:

• Use encouragement. Make the fault seem easy to correct.
• Make the other person happy about doing what you suggest.

Carnegie suggests for the eighth point that you surface a flaw in your own proposal that is easy for the hearer to correct. When the hearer recognizes the easy solution, he begins to have some emotional connection to the idea. He begins to embrace your idea as his own idea, and then (in the ninth point) is happy to do what you suggest.