Maine Coon keeps sitting outside my house crying at my cat?

I have a young female cat, who is quite shy. Recently a maine coon (who i am not sure whether is stray) has persistently come outside my house and sometimes even into the house. At first I was worried it was a stray and felt sorry for it, so I gave it food. But it didn't even eat the food and just wanted to get to my cat. It sits outside crying all day and night and I don't understand why?