Why should you not drink carbonated drinks after getting a tooth extraction?

No reason: There is no contraindication to drinking a carbonated drink as long as you are just swallowing it. However, there is no nutritional value to it either.

Acidity: Carbonated drinks usually have a very low ph and can be irritating to the surgery site. Also, i tell patients no carbonated drinks because they tend to drink them with a straw. The positive pressure in your mouth you create when drinking with a straw can dislodge the bloodclot leading to complications later.

It is fine: Carbonation will not negatively effect the extraction site, due to ph or any ingredient: it is how one ingests the drink that matters: no straw, as suction (negative pressure) can dislodge a clot, leading to a "dry socket" a very painful problem.