Using the phrase "begs the question" to mean "raises the question" is a common misuse of the term. In academic and professional writing, "begs the question" actually refers to a logical fallacy where a statement assumes the truth of the conclusion it is attempting to prove. To avoid confusion, it's best to use "raises the question" when you want to indicate that something prompts or suggests a question.
An example:
"Vintage furniture is better than new furniture because it’s usually made from real wood."
This statement relies on the assumption that real wood is the superior material for furniture. However, nothing in this claim explains why that’s the case, so it begs the question, “What makes real wood better than other materials?”
I don't understand the Mike Tyson reference though.