Can I invite you? No? Why not?
Extended hand in front of me* - I've been trying to invite you all night! Would you like to dance? - No, thank you. I usually prefer cabeceo. - Oh, but I tried cabeceo, and it really didn't work! So I came to ask. - Oh, but cabeceo DID work. ____________________
Tango has its (behavioural) codes and they are there for a very good reason. Cabeceo, or invitation with your eyes, is one of the most important and surely one of the most useful ones!
Make sure you know about cabeceo and other codes before you hit the dance floor! They can really make your tango life a bliss if you know and use them well! :)