ok here, thanks to rika awesomeness this is how we start to know more about "kodaka" issues
kobato is just a mirror for kodaka she suffer from the same problem of him: being unable to handle with be "sociable", just rewatch episode, 10 13:30 to 15:20 and see the final of the same episode then rewatch episode 11 and and each piece of the puzzle will fit Kodaka revealing the problem until then had been kept hidden.
kodaka true want friends but he can't true handly with then, the only way he can have friend is the way who he keeping using by keep hiding from the girls(rika is the one who find about this) about their already being friends, it's just not the marriage or confession his issues but the whole picture.
kodaka make clear who he want a girlfriend but like the friend he can't handly, another note if indeed kodaka dont want girlfriend or marriage why he not yet asked to pegasus to cancel the marriage contract between pegasus and his father, he just keep curling the answer he never true goes to pegasus and ask to cancel this since he learned about.