help explaining this 'bad' behaviour?

Not bad really just being a horse...
My friend Steff has been riding Kitty occasionally for a few months. Kitty likes her. Steff's a bit ineffectual but tries hard to understand she sits well and is persistent if not always clear in her signals.
we went out for a ride this week and decided to go up one combe, across the top of two others and down the fourth. As we passed the top of the second combe Kitty set off the shortest way home and Steff couldn't do anything about it. They disappeared across the hill at a walk with Steff obviously trying to turn and Kitty totally ignoring her. I waited, and in a few minutes they appeared at a canter coming back to me. Steff let Kitty slow to a walk a hundred yards from me and Kitty immediately turned around and carted her off at a walk again. This happened 3 times before she could finally properly rejoin me and blow me if it didn't happen exactly the same at the top of combe number 3!

Now, I know Kitty was trying to say lets go home the short way, but why was she so determined when she hasn't done it before, she wasn't upset or stressed (she never broke out of a walk), she usually takes note of Steff and she usually follows me and Dancing anyway, even if she has no rider at all?

That is strange, isn't it? Wish I had some answers for you. Fanny can be very much like that, but for me it's because I am not asking her the right way. I've been told that I'm too "soft" on horses when I ride, and that they don't respect me. Same thing happens when I ride school horses - they don't "listen" to me very well, while some little kid whose feet barely reach the sides of a horse can ask it to go anywhere and do anything and it complies willingly. Sorry, I'm rambling and not helping you at all.

i do wonder actually if Kitty doesn't respect Steff - even though she likes her. Kitty seems often to think she knows best with Steff but then why leave me when she always stays with me when she is following loose?

So long as your friend Steff was ok and not scared, this sounds like a horse with a sense of humour! I bet a gelding wouldn't have thought up this caper. It is odd as she kept coming back, but I think that you are right about her not respecting Steff. She was probably giving her opinion but obviously still had a connection with you and changed her mind.