Jehovah's Witnesses believe that dating should only happen when one has an intention of getting married, it is not something that is done for recreation purposes. When it comes to Dating and ulimately marriage, JW's follow the words of 2 Corinthians 6:14 " Do not be unequally yoked with unbelievers. For what partnership has righteousness with lawlessness? Or what fellowship has light with darkness?"
Although they will not say it to your face, you as a non Witness are an unbeliever and are unrighteous and lawless or at the very least, capable of these thigs at any moment and will ultimately pull the JW into your unbelieving ways.
JW parents view the marriage of their Son or Daughter to a non Witness as a catastrophe second only to death or being disfellowshipped. The girl you are interested in is likely being warned not to be swayed by your cunning worldly ways and that even though you may seem like a nice guy you don't love Jehovah and are therefore under the influence of Satan as is the rest of the world. This is not an exaggeration. They will site the experience of Dinah in Genesis Chapter 34 as an example of the disastrous things that can happen when one of God's followers trusts an unbeliever.