I've been there and I know it sucks. Haven't ever actually gotten around it, but this is my humble piece of advice:
As others already mentioned, if she comes when you call and everything is fine when you are together, you're probably making a big thing out of nothing.
But I do get it that it is just fucking tiring being the only who has to arrange it: find a good day, the right time and always look for a new and good place to go. You just want for once to fucking sit back, get the suggestion and just say yes or no, and not do all the work by yourself.
So no, I don't think it necessarily comes from insecurity.
The thing is that with dating, as with almost everything in life that involves any social encounter between two people, the way you do something during the very first encounters sets the rythm any future encounters. Meaning that if, for example, you make a new friend tomorrow that you two go together climbing from now on, and you are the one calling him the first 2-3 times to arrange climbing, don't expect in the future that he will ever call you about it. You have already set the rythm, and that is that you call and suggest it, so he expects from you to do it in the future again. That's how the dynamic between the two of you has now been set. Doesn't mean he doesn't want to go other times, means that's the system that has now been imprinted in his brain.
If you wanna change that, he has to now make a cognitive choice to bypass it. When it's a friend as in the example, abstaining a little from arranging it will probably work. When he realizes you haven't arranged anything chances are he will hit you, curious why the two of you haven't arranged anything. Consciously, he has now started realizing that it was always your initiative, it had also been simple and easy for him. If you really wanna change that, at that exact point is your opportunity, but it is a tricky part and you have to play your cards right. The impression he now has to get is that you had serious reasons you didn't call but if he had called himself it could had worked out. Be prepared that at that point you might lose your climbing buddy. He might not be willing to change the simple and easy way he was used to and just let things flow.
With dating it is a little bit more complicated, because of the man-woman dynamic. Also, girls like the easy thing and not put too much effort and thinking to these kind of stuff. She might never ask why you haven't arranged anything or it will feel like never
, but most probably she will. It will take more time than you probably are able to abstain. And even when she does it is so tricky to fake the reason you actually abstained from arranging anything! Maybe a playful "don't know, I actually wanted to, but couldn't figure out any good new suggestion. Damn you've drained me girl! " would send the message without letting the bitterness come out. If the girl has invested emotionally, which seems like she has, it is harder to "lose her" than your climbing buddy, but it will be a damn slow and painful process.I actually think that it will be a good thing to reset the dynamic. It will take away this pressure from you and secondly, she will invest more and realize she has to do some of the work if she wants to see you. Just don't neglect, that when you will make her take initiative for once, it doesn't automatically set the dynamic you want, but it sets it back to zero. Now is the time to set the new one and make it a fair one, don't go to the other side cause she will notice and might start thinking something has changed and you don't like her that much any more and blah blah and that can be unpredictable.
Btw girls aren't so much practiced to arranging dates as we are, so chances are she is gonna fuck it up, but nevertheless if you decide to, go for it.
This is also a bit of a sticking point for me, so if anyone has any other suggestion...