What does it mean a guy gives you the signs that he likes you but says no to go to the dance with you?

If a man wont go out in public it's because he is embarrassed to go out with you where others can see you or he is dating someone else and does not want to be seen with you. Either way, it is probably not good. If a man likes you, he will be thrilled to go to the dance with you.
I suggest that you buy a copy of "The Rules" for women. I believe it is out of print, but it is spot on!
I am a guy, and when I was dating I purchased a copy of "The Rules" for women, to know how women think. I now have a daughter and I gave her a copy of this book.
Guys will do anything to be with a woman if he really likes her. He will call! He will buy! He will go to the dance with you! If he doesn't, move on!
Good luck and God bless