As far as I've been able to read, nothing in the Treaty of Pressburg, or really anything following the War of the Third Coalition obligated Francis to take that action. I also know that Francis also made himself Emperor of Austria, and held that title simultaneously with that of Holy Roman Emperor for three years. Was creating the former Empire in anticipation of losing the latter title? Or did Francis initially seek to keep both? Even so, why give up such a prestigious title when nothing forced him to do so?
Though I believe that we don't have a first-hand account for the exact reasons behind Francis II's abdication, I would be putting in the opinion of Peter H. Wilson regarding how the abdication was taken in by the differing imperial vassals at the time.
Wilson, in the book "Heart of Europe", mentioned that "Austrian Ministers carefully phrased the abdication patent to blame the new Confederation of the Rhine for having already wrecked the Empire, reducing Francis' act to simply releasing his vassals from their feudal ties."
Essentially, Francis' dissolution of the HRE was a symbolic act meant to discredit Napoleon's new political entity in Germany by portraying it as a symptom of the destroyer of the Old Order in Central Europe. Essentially, Francis wanted to have his title of Austrian Emperor as the sole image of a defiant German power against Napoleon's might. During the abdication, Austria's allies actually argued that the Holy Roman Empire was still intact though occupied by a foreign power, though by de facto, the Holy Roman empire and its myriad of institutions were systematically retired starting with the Abdication of Francis II and the start of the institutions of the Confederation of the Rhine, which continued on as the German Confederation after the Congress of Vienna rearranging Europe after the Napoleonic Wars.
I have not seen any other plausible explanations aside from Wilson's and I fear putting in my own assessment since I'm not really a acquainted with late Holy Roman Empire legal history, sadly.