Eh, I can buy it. Had she said "I don't have those same feelings, can't we still be friends/partners" it would be one thing. But pretending it didn't happen CAN appear to some as not at least respecting their feelings.
As far as Castle's secret, well he's doing it to protect her. She's only safe if she doesn't investigate any more... and by safe I mean NO FLIPPIN' HIGH-PAID ASSASSINS coming after her. And of course not risking the lives/safety of those around her.
It's not a great thing he's doing, but their a life-saving reason.
Though in Kate's defense, she's probably trying to save the both of them the pain of a (potentially) failed relationship and thus the end of their friendship/partnership.