Hello anon :) 

I think the easiest answer is ‘because he was bored’ but I think it’s more than that. For sure, he didn’t had any interest in Mayuko, romantically nor sexually. 

However he noticed that she was totally in love with Hatori. 

He even said ‘why don’t you just go steal him from her’

For me, Shigure definitely wanted Hatori to be with Mayuko instead of Kana. Probably because he knew that Kana would be too weak for the weight of the curse. He knew that Kana and Hatori would have never lasted. 

If you saw episode 15, you will notice that Shigure, instead of Ayame, did not say to Hatori to get Kana back but instead 

He knew that Mayuko is good for Hatori, she is strong willed enough to support Hatori as he need, because he is sensible and selfless, and she desire nothing more but his happiness. I would even say that Shigure and Mayuko are similar in that way. 

So I think that Shigure did go out with Mayuko so later when Hatori and Kana would broke up, Shigure would help Mayuko to be with Hatori. 

Here Shigure telling to Hatori he was going to send photo of Hatori doing the dance to Mayuko, and Hatori asking if the two of them are back together, provoking Shigure to laugh at him. He is totally trying to hook them up.