Please, not so puzzle thoughts!
More simply:
1). p-Aminophenol is insoluble in water but as having an amine group, p-aminophenol can form a p-hydroxylphenylammonium chloride salt, which is soluble in water; therefore, HCl is dropwise added, up to complete solvation.
2). p-Hydroxylphenylammonium chloride is a salt of a weak base (p-aminophenol) with a strong acid (HCl) and thus, it is acidic and not fully ionized but it exists in equilibrium of the ionized with the unionized form (p-aminophenol + HCl).
3). The reactivity order of acetic anhydride is: amine > phenol > water, respectively.
4). Thus, the unionized form of p-aminophenol,HCl selectively reacts with acetic anhydride anhydride and forms acetaminophen (= Paracetamol) + HCl + acetic acid.
5). Once acetaminophen is formed and according with the Le Chatelier principle, the equilibrium is driven to further deionization and so, the reaction goes on.
6). But the so formed HCl can simultaneously catalyze the esterification of p-aminophenol, as well as the hydrolysis of acetic anhydride.
7). AcONa is a salt of a strong base (NaOH) with a weak acid (AcOH) and apart existing in equilibium, it is quite alkaline and thus, it can neutralize the liberated HCl, avoiding the simultaneous formation of side products.
. By writing all involved reactions and their products on a piece of paper, you will immediately clarify the issue by yourself.