I have the suspicion that their intention was to mock the press. They were implying that the press usually behave like children and that the press will need to behave for the President, the so called "adult in the room". However this is backfiring on them when Brandon is exhibiting lack of cognitive ability.

I found a mention of "big boy press conference" on the whitehouse press briefing transcripts from July 2.

Q — a logistical one, which is you mentioned the press conference.

MS. JEAN-PIERRE: Yeah.

Q Is that going to be kind of a real, big boy press conference that we’re used to, or —

MS. JEAN-PIERRE: (Laughs.) Did you say “big boy press conference”? (Laughter.)

Q Yeah, like one of these two-and-twos tha- — that might be a little more limited.

MS. JEAN-PIERRE: So, I believe — and I know you guys are holding me to it — it is a — I believe it’s a solo press conference. We’ll certainly have more to share with all of you as we get closer —

Q And then more —

MS. JEAN-PIERRE: — to next week.

Q More thematically —

Q We should call it the big boy (inaudible). (Laughter.)

MS. JEAN-PIERRE: Yeah, I was about to say “big boy” Justin over here —

Q Yeah, yeah.

https://www.whitehouse.gov/briefing-room/press-briefings/2024/07/02/press-briefing-by-press-secretary-karine-jean-pierre-july-2-2024/

So the conference was originally announced on July 2 and it's not going to happen until July 10. How long does it take Big Boy Brandon to prepare for 1 press conference? 8 days.