People I do get you're angry, Shizuka also broke my heart. But I do realize she's not evil. Like, what would you have done in her situation? I think she really likes Mio and is doing her best to get over Kaoru. She could have opened up more, but I really think she just really wanted to get over...
The "kind of forcefull invitation" refers to the fact that she's probably going to confess, like, in a very strict and old-fashoned way.
For Shizuka, I'm pretty sure she's trying her best to get over Kaoru (she also promised herself never to go back to her). I think she likes Mio but is still...