Why is it ill advised to eat the solid aspirine formed from salicylic acid + acetic anhydride In the laboratory notes it is indicated that it is ill advised to eat the solid formed from this experiment. An esterification reaction, in which salicylic acid is treated with acetic anhydride.

If it is for the acid added as catalyst either sulfuric acid or phosphoric acid. Why isn't it possible to neutralize it with a strong basic?

The addition of water should be enough to quench (destroy) any remaining acetic anhydride and turn it into acetic acid, and this latter one is more soluble than aspirin so it should be possible to crystallize aspirin without any acid.

The question appears in this lab notes http://www2.xula.edu/chemistry/crs-orgleclab/Organic_Lab_1_2230L_Web_Files/23_Aspirin_notes.pdf

I think it is self-evident that your basement shouldn't become a pharmacy. I think it has more to do with the acids used in the synthesis. Does the industrial process differ from the synthesis presented in the article with regards to this aspect (acid catalyst and their neutralization after the process)?
Unless you worked to Pharma industry Good Manufacturing Practice you shouldn't trust your product

The simple reason why you should not trust the product is that that you don't know it is safe unless you have followed rigorous quality control processes. The drug industry follows carefully regulated quality-control processes known, in Europe, as Good Manufacturing Practice. This is far from easy to meet and even major drug firms sometimes have their factories closed because they fail to ensure it.

For your particular reaction there are many possible things you would need to check before knowing the product was safe to consume. You really don't want to guess whether all the acetic anhydride or acetic acid has been removed: even a small amount will be bad for you (you can't rely on intuition that it should all have been removed). And are you sure there are no nasty side products? Have you checked? Have you checked the purity to make sure? Have you had a check by an independent party?

If you can't say yes to all of these (and more: go read the GMP standards for aspirin manufacture), don't take the product.