In most of bikes seat tube is 'sticking out' 1 inch above the top tube (assuming the top tube is parallel to the floor), in my bike however it is not (C-T is almost equal to C-C).
So if I want to compare my bike to other bikes, I have to add 1 inch when measuring C-T so actually the frame is 24" not 23".

And because (according to most charts and calculators) I need 22" frame (that's C-T) - that explains why I had the feeling the bike is too big for me.
The top tube is too long as well - I'm not comfortable when holding the 'bullhorns'.
The smaller the frame, the shorter the top tube.
I'm going to aim in 22" frame then. Let the basketballs hang low.