He just won the case for the defense. Why would they want to impeach his credibility?
The point is to impeach Blasted Bicep Boy's testimony relating to his own actions. He was testifying that he was not chasing Rittenhouse, was not moving to shoot him, was not intentionally pointing his gun at him, and wouldn't have shot him regardless because of his medical oath.
If the defense had pointed out that his routinely carrying a loaded firearm specifically for the purpose of self defense conflicted with his stated position of "do no harm" and being unwilling to injure or kill someone then it calls into deeper question the truth of his statement about chasing Rittenhouse, moving to shoot him, and intentionally pointing a gun at him. Same reason they're trying to get his roommate's post about BBB saying his only regret was not emptying his gun into Rittenhouse admitted into evidence.
Earlier, there was another potential "gotcha" where BBB testified that he was not protesting and as a medic was treating people without respect to their affiliation, but also can be heard on the video calling out Rittenhouse for offering to help an injured protester because "we have our own medics". I didn't think that was as impactful and didn't mind them missing out on that. Of course, they did connect the dots on some of his hard left affiliations.