Well, then don't.
I don't know about "funny" but more amusing. I doubt anyone was ROFL instead of "oh snap!"
I thought it was amusing because it is unexpected. (And how brutal it was.) You expect something stupid or "funny" from Quagmire in response. You do not expect a complete and serious outlined tearing down of just how much of a terrible person Brian is. Everything that is not redeeming about the character outside of his strange relationship of Stewie was listed.
But in the end, it's amusing for the same reason Brian getting back at Peter years later for rolling up the window or months later for the vicious beating Stewie gave him. It's not expected. Next week, the deconstruction of the character will be forgotten and more expected things will occur. It's clever because it rewards twice for being a regular viewer of the show. It rewards you for having past knowledge of the show, and then rewards again by subverting what you expect the show to do based on the past knowledge of what they normally do. Properly doing double layered humor can be difficult, but someone on the writing staff does have a knack for it and I assume they were involved in Handi-quacks as well.
And in that regard and others, it was the last part of the episode one should criticize. Indeed, it's the antithesis of the standard problem with Family Guy. It was essential to one character, Brian was a required component of it. It was entirely self-contained into the details of Family Guy itself. (Outside of the accurate description of that terrible book, Catcher in the Rye.) And it was well thought out, time was spent on it, a careful hand was applied.
No, it's not on par with say, the "causality loop explanation" from Bender's Big Score or "Eternal Moonshine of the Simpson Mind". But, in the scope of Family Guy, FOX's Animation Domination, and the McFarlane Empire, it's needed. They would do well to mine the mentality that led to its inclusion.