Hi Denisa,
Yeah, so that's not correct... if you buy a song on iTunes, you are buying it for personal use only... as soon as you attach it to a video and post it online, it becomes commercial use (even if you don't make any money)... that's why YouTube and Facebook actually do copyright music checks on all videos. YouTube will take your video down if you have copyright music on it.
YouTube actually has a library of music anyone can use on their videos here - you're more than welcome to use any in this list here..
Otherwise Google Royalty-free music, and avoid any sites that ask you to pay a monthly or yearly subscription...
Does that make sense?
Also... the artist might absolutely feel that you're improving their song or making it better with dance moves, but their publisher/record company just wants all the money it can get... it wants people to buy their song or watch their music video... so that's where it gets tricky. It's a complex thing, but there is lots of royal-free music out there that the artists would love you to use in your videos.