I don't think it's rude but some people may look at it as a sign of insecurity. They may think down the line you are going to constantly "require them to say or do things to prove their love."
Most of us assume a person knows his or her own feelings.
The only reason we'd ask them to tell us "why" is because we either don't believe them or we're fishing for compliments.
Another possibility is we want to make sure that we define the meaning of love in the same way.
If one is intent on asking the question the best way to do so is probably while you're snuggling together.
"I don't want you to take this wrong way but I need to know what is about me that caused you to fall in love?"
Truth be told we can ask any questions we want to if we are willing to ask them in a way that doesn't put the other person on the defensive.