Hangman Page explains why he calls it the AEW MEN'S World Championship and why it's important to distinct the Men’s and Women’s titles:

“It's an important distinction because it does put them on the same level. Our Women's roster in AEW is incredible. They are just as, and in many cases, more talented than many on the Men's roster.

I think our fans connect with them in a way just as equally as they do with us. To have two divisions, a Men's and a Women's division, but to have to call one by the Women's World Championship and the other as if it's the more important one, you don't make the distinction.

I feel like that's not how we present our rosters on television, so why should we refer to the championships in that way either? I'd like to think at least that we don't present the men and women as being on different playing fields in AEW.

It’s just a personal choice that I hope other people take up, and I've noticed it happening a little bit and I hope that continues."